The complex solutions to the given equation are -1 + i√2 and -1 - i√2.
To determine the complex solutions to the equation, we can first simplify the quadratic equation by dividing each term by 2. This gives x² + 2x + 3 = 0.
The discriminant (b² - 4ac) can be calculated to find the nature of roots.
b² - 4ac = 2² - 4(1)(3) = 4 - 12 = -8
As the discriminant is less than 0, the roots are imaginary roots. That is, the roots are complex numbers.
To find the roots of this quadratic equation, the following steps can be followed.
Since the coefficient of x² is 1, the quadratic formula can be used to solve the given quadratic equation. The quadratic formula is given by
x = [-b ± √(b² - 4ac)] / 2a
Substitute the given values into the formula.
x = [-2 ± √(-8)] / 2
On simplifying the above expression,
x = [-2 ± 2i√2] / 2= -1 ± i√2
Therefore, -1 + i√2 and -1 - i√2 are the complex roots or solutions of the given quadratic equation.
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If 3 boxes of cereal cost $4.50, what does 1 box of cereal cost?
Answer:
$1.50
Step-by-step explanation:
3 boxes = $4.50
1 box= $4.50÷3
1box= $1.50
Answer:$1.50
Step-by-step explanation:
The line 8-2y=x is dilated by a scale factor of 1/4 about the center. What is the equation of the image
The equation of the image is x = 32 - 2y which is dilated by a scale factor of 1/4 about the center.
What is dilation?Dilation is a process for creating similar figures by modifying the dimensions.
To dilate a line by a scale factor of 1/4 about the center, we can first find the coordinates of the center of dilation.
Since no center is given in the problem, we can assume that the center is the origin (0,0).
To find the equation of the image, we need to apply the dilation to the original line. The dilation multiplies all distances by the scale factor, so the image of the point (x, y) is (1/4)x, (1/4)y).
So, the image of line 8 - 2y = x under this dilation is:
8 - 2(1/4)y = (1/4)x
8 - (1/2)y = (1/4)x
32 - 2y = x
Therefore, the equation of the image is x = 32 - 2y.
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Simplify. Assume ((3c^(2))/(2d^((8)/(5))))^(4) Write your answe that have no varia
The answer is ((81c^(8))/(16d^((32)/(5)))).
To simplify ((3c^(2))/(2d^((8)/(5))))^(4), we can use the power of a power rule and distribute the exponent of 4 to each term inside the parentheses.
((3c^(2))/(2d^((8)/(5))))^(4) = (3^(4))(c^(2*4))/(2^(4))(d^((8*4)/(5)))
Simplifying further, we get:
= (81)(c^(8))/(16)(d^((32)/(5)))
= (81c^(8))/(16d^((32)/(5)))
This is the simplified answer with no variables. It cannot be simplified further. Therefore, the answer is ((81c^(8))/(16d^((32)/(5)))).
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Find a polynomial function whose graph passes through (7,13), (9,- 11), and (0,3).
Step-by-step explanation:
I am going to assume this is a quadratic so
[tex]f(x) = {ax}^{2} + bx + c[/tex]
When 3 is c
[tex] {ax}^{2} + bx + 3[/tex]
When x is 7,
[tex]a( {7}^{2} ) + b(7) + 3 = 13[/tex]
[tex]49a + 7b = 10[/tex]
When x is 9,
[tex]a(9) {}^{2} + 9b + 3 = - 11[/tex]
[tex]81a + 9b = - 14[/tex]
We have two system, let's eliminate the b variable by multiplying the second system by
[tex] \frac{7}{9} [/tex]
[tex]63a + 7b = - \frac{98}{9} [/tex]
Bring down the first system
[tex]49a + 7b = 10[/tex]
Subtract the two system,
[tex]14a = \frac{ - 188}{9} [/tex]
[tex]a = - \frac{94}{63} [/tex]
Plugging in a, we will eventually get
[tex]b = \frac{748}{63} [/tex]
So our quadratic is
[tex] - \frac{94}{63} {x}^{2} + \frac{748}{63} x + 3[/tex]
The cost of renting a canoe to use on River Y costs $25. The cost of renting a canoe to use on River Z costs $2 per hour plus a $11 deposit. The total cost, c, of renting a canoe on either river for n hours can be represented by an equation. Write and graph a system to find how many hours you have to rent a canoe for the cost to be the same on both rivers.
0.2=1−(1−T1)30T=135 answer
The solutions to the given equations are T1 = 0.2 and T = 4.5.
To solve the given equations, we will use algebraic methods to isolate the variable on one side of the equation.
First, let's solve the equation 0.2=1−(1−T1).
0.2 = 1 - (1 - T1)
0.2 = 1 - 1 + T1
0.2 = T1
So, T1 = 0.2
Next, let's solve the equation 30T=135.
30T = 135
T = 135/30
T = 4.5
So, T = 4.5
Therefore, the solutions to the given equations are T1 = 0.2 and T = 4.5.
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4. Use the Variation of parameters to find a particular solution for the ODES et 22 (a) y" – 2y' + y = (b) y" + y = = sec(x) (C) y" + y = sin?(x) =
The Variation of Parameters is a method used to find a particular solution for ordinary differential equations (ODES). The method involves finding the general solution to the homogeneous equation and then using that to find a particular solution to the non-homogeneous equation.
For the given ODES:
(a) y" - 2y' + y = et^2
First, we need to find the general solution to the homogeneous equation y" - 2y' + y = 0. The characteristic equation is r^2 - 2r + 1 = 0, which has a repeated root r = 1. Therefore, the general solution to the homogeneous equation is yh = c1e^t + c2te^t.
Next, we use the Variation of Parameters to find a particular solution. We assume that the particular solution has the form yp = u1e^t + u2te^t, where u1 and u2 are functions of t. We then find the first and second derivatives of yp and substitute them into the original equation. After simplifying, we obtain a system of equations for u1' and u2'. We solve for u1' and u2' and then integrate to find u1 and u2. Finally, we substitute u1 and u2 back into the equation for yp to find the particular solution.
(b) y" + y = sec(x)
Similarly, we first find the general solution to the homogeneous equation y" + y = 0. The characteristic equation is r^2 + 1 = 0, which has complex roots r = i and r = -i. Therefore, the general solution to the homogeneous equation is yh = c1cos(x) + c2sin(x).
Next, we use the Variation of Parameters to find a particular solution. We assume that the particular solution has the form yp = u1cos(x) + u2sin(x), where u1 and u2 are functions of x. We then find the first and second derivatives of yp and substitute them into the original equation. After simplifying, we obtain a system of equations for u1' and u2'. We solve for u1' and u2' and then integrate to find u1 and u2. Finally, we substitute u1 and u2 back into the equation for yp to find the particular solution.
(c) y" + y = sin^2(x)
The general solution to the homogeneous equation y" + y = 0 is the same as in part (b). We use the Variation of Parameters to find a particular solution in the same way as in part (b), but with the right-hand side of the equation being sin^2(x) instead of sec(x).
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Find a positive value of c so that the following trinomial is factorable. x^(2)-4x+c
Find a positive value of c so that the following trinomial is factorable. [tex]x^2-4x+c[/tex], The value of [tex]c[/tex] will be given by [tex]c=4[/tex].
To find a positive value of c so that the trinomial [tex]x^2-4x+c[/tex] is factorable, we need to use the formula for the sum of two squares. This formula states that [tex](a-b)^2=a^2-2ab+b^2[/tex].
In this case, we can let [tex]a=x[/tex] and [tex]b=2[/tex], so the formula becomes [tex](x-2)^2=x^2-4x+4.[/tex]
Comparing this formula to the given trinomial, we can see that the value of c must be 4 in order for the trinomial to be factorable.
Therefore, the positive value of c that makes the trinomial [tex]x^2-4x+c[/tex] factorable is [tex]c=4[/tex].
In factored form, the trinomial becomes [tex](x-2)^2[/tex].
Answer: [tex]c=4.[/tex]
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Test Prep Dono Dashbour e Unite Unit Activity: The Definite Integral 5 of 8 E Save Task 1 Print or You are learning the landscaping trade as an apprentice for 1plus1 Landscaping. Your supervisor wants you to calculate the area between the curved edge of a garden bed and the side of the house. Using the area, he can calculate the amount of mulch he will need for this job. Your supervisor has not yet provided an equation for the curve. Instead of waiting for the equation, you start a spreadsheet that will aid in the calculation. When you receive the equation, you'll have only a small amount of work to do in order to compute the area that he wants to cover with mulch. Part A Because you don't yet have an equation from your supervisor, choose one to help you set up the spreadsheet. ater, modify the spreadsheet when you receive the actual equation. Use spreadsheet software to: • Estimate the area that lies under the curvey -x + 1 between x = 0 and x = 10 Let the number of sub-intervals ben=5 . First calculate the area using left endpoints and then right endpoints
The area under the curve is 4.55 square units.
Here we have to find the area,
That lies under the curve y -x + 1 between x = 0 and x = 10
Therefore,
To estimate the area that lies under the curve y = -x + 1 between x = 0 and x = 10,
Use the Riemann Sum method,
Divide the interval [0, 10] into n subintervals of equal width,
And let Δx be the width of each subinterval.
Then, we can estimate the area under the curve as the sum of the areas of n rectangles with heights given by the function.
The formula for the Riemann Sum is,
⇒ Δx [f(0) + f(Δx) + f(2Δx) + ... + f((n-1)Δx)]
where Δx = (b-a)/n, a = 0, b = 10, and f(x) = -x + 1.
Let's choose,
n = 100 for a reasonably accurate estimate.
Then, Δx = (10-0)/100 = 0.1
Put it into the formula, we get.
⇒ 0.1[1 + 0.9 + 0.8 + ... + 0.1]
Evaluating the sum using the formula for the sum of an arithmetic series, we get:
⇒ 0.1(0.5)[2 + (99)(-0.9)]
Simplifying, we get,
⇒ 4.55
Therefore, the required area be 4.55 square units.
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You are planning to sell children's fairy wings at a craft fair. It costs you $5 in supplies to make each set of fairy wings and you will sell them for double your cost.
You have 100 sets of fairy wings and sell 60 of them by 2pm. The craft fair ends at 4pm and you want to sell the rest of your wings faster so you mark the price down by 30%.
With c = supply cost to make a set of wings, and P(c) = price, the equation for the price you first sell the wings is A) P(c)=2c B) P(c)=.7c C) P(c)=.5c D) P(c)=1.5c
The new equation to sell the wings faster with N(p)=new price is A) N(p)=.3p B) N(p)=p-.3 C) N(p)=.7p D) N(p)=.5p
The composed equation N(P(c) is A) .9c B) 1.4c C) .7c D) 2.7c
and represents A) the markup of the discounted price over your supply cost B) your markup profit on all the wings C) how much money you will lose by selling the wings at a lower price
The domain of all the functions is A) [0, infinity) B) (-infinity, 0] C) (-infinity, infinity)
because A) the prices will always be positive numbers B) the wings make it possible to fly C) you can hace any possible answer in these questions D) anything is possible
Answer: Dragonfly wings for the boys cost $1 while fairy wings for the girls cost $2. Phoebe's mom spent $18 on the gifts. How many dragonfly wings and fairy wings
Step-by-step explanation:
Answer:
The answer to the first question is A) P(c) = 2c, because the wings will be sold for double the cost of supplies.
The answer to the second question is B) N(p) = p - 0.3, because the price will be marked down by 30%.
The answer to the third question is A) 0.9c, which represents the markup of the discounted price over the supply cost.
The domain of all the functions is A) [0, infinity), because prices and costs must be positive numbers. Therefore, options B, C, and D are incorrect.
6. What is the length of side AB?
AB =
BC = 2x
T.P. =>
4x² = x² + 6²
3x² = 36
x² = 12
=> x = 2sqrt3
What is the area of the notebook paper?
Answer: 8.5 by 11 inches.
Step-by-step explanation:
The standard 8.5″ x 11″ or Letter size so prevalent in full sized notebooks.
Can you please give and explain please. I dont get it
Answer: a = 3, b = 2
Step-by-step explanation:
When a system of linear equations has no solution, they are parallel and do not share the same y-intercept.
Parallel lines have the same slope so a must equal 3.
The first equation's y-intercept is -2, so the only other option is b = 2.
Hope this helps!
the differenceof two numbers is -1 if twice the first number ids added to three times the second number the result is 13 what are the numbers?
The numbers are 4 and 5, as their difference is -1 and adding 2 times the first to 3 times the second results in 13.
To solve the problem, we can start by using algebra. Let x be the first number and y be the second number. Then we can write two equations based on the given information:
x - y = -1 (since the difference of the numbers is -1)2x + 3y = 13 (since adding 2 times the first to 3 times the second gives 13)We can solve this system of equations by substituting x - 1 for y in the second equation, which gives:
2x + 3(x-1) = 13Simplifying this equation, we get:
5x - 3 = 13Adding 3 to both sides, we get:
5x = 16Dividing both sides by 5, we get:
x = 4Now that we know x, we can use the first equation to find y:
4 - y = -1Adding y to both sides, we get:
4 + y = 1Subtracting 4 from both sides, we get:
y = 5Therefore, the first number is 4 and the second number is 5, which satisfies both equations.
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Please help in math 75 points
Answer
10 is the answer
Please mark as brainliest HOPE IT HELPS!
A teacher can grade 15 papers in 25 minutes. At this rate, how many papers can she grade in 90 minutes?
15/25 = x/90
25x = 1350
x = 54
54 papers
A water park sold 2,640 child tickets and 1,360 adult tickets. What percentage of the tickets sold were child tickets?
Answer:
66%
Step-by-step explanation:
"of the" something = means denominator of a fraction
of the tickets sold = denomination here
question asked about child tickets , so child tickets = numerator here
what percentage? = fraction x 100%
answer:
2640 / (2640+1360) x 100
What is the solution for 3 1/4 + 3/8
Result in decimals: 3.625
Step-by-step explanation:
Answer:
29/8 or 3 5/8
Step-by-step explanation:
first turn 3 1/4 to 13/4
now change 13/4 to get 26/8
now add 26/8+ 3/8 and get 29/8 or 3 5/8
in a certain town there were 171 robberies last year . this year the number of robberies has gone down 39%. how many robberies were there this year , to the nearest whole number ?
The robberies that took place this year to the nearest whole number is 104 robberies.
What distinguishes a percent reduction from a percent difference?A value's percentage change from its initial value is expressed as a percent reduction, but the percentage difference between two values is expressed as a % change from their average.
Let us suppose the number of robberies this year = x.
Given that,
This year the number of robberies has gone down 39%.
x = 171 (1 - 39/100)
x = 171 (1 - 0.39)
x = 104.31
Hence, the robberies that took place this year is 104 robberies.
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Using Pythagorean theorem, solve for x. Please, please help.
Answer: 14.6
Step-by-step explanation:
Kate buys a greeting card for 3.79. She then buys 4 postcards that all cost the same amount. The total cost is 5.11. How much is each postcard? Show your work.
Answer:
$0.33
Step-by-step explanation:
5.11-3.79=1.32÷4=.33
What’s the value of -√22
Answer:
the answer is 22
Step-by-step explanation:
-22 x -22=22
(w^5y^4)^3
show work pleaseee
Using the properties of the exponents, we solve the expression and found the result as [tex]w^{15} y^{12}[/tex].
What are exponents?The exponent of a number indicates how many times a number has been multiplied by itself. Exponent is another name for a number's power. It could be an integer, a fraction, a negative integer, or a decimal. How many times we must multiply the reciprocal of the base is indicated by a negative exponent. When writing exponentiated fractions, negative exponents are employed. A fractional exponent is one where the exponent of a number is a fraction. Parts of fractional exponents include square roots, cube roots, and nth roots. The square root of a base is a number with a power of half.
Given,
[tex](w^5 * y^4)^3[/tex]
We have to solve this using the properties of the exponents.
Now, this can be written as:
[tex](w^5)^3 * (y^4)^3[/tex]
When the exponent is raised to another power, we can follow the power rule for exponents.
This rule states that multiply the exponent by the power to raise a number with an exponent to that power.
Then the above expression becomes
[tex]w^{(5*3)} * y^{(4*3)}[/tex] = [tex]w^{15} y^{12}[/tex]
Therefore using the properties of the exponents, we solve the expression and found the result as [tex]w^{15} y^{12}[/tex].
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Evaluating a quadratic expression: Integ Evaluate the expression when c=3. c^(2)-5c+2
The value of the expression c^(2)-5c+2 when c = 3 is -4.
Evaluating a quadratic expression involves substituting the given value of the variable into the expression and simplifying. In this case, we are given that c=3 and the expression is c^(2)-5c+2. We will substitute 3 in for c and simplify.
Step 1: Substitute 3 in for c: (3)^(2)-5(3)+2
Step 2: Simplify the expression: 9-15+2
Step 3: Combine like terms: -4
Therefore, the value of the expression when c=3 is -4.
A quadratic term is any expression that has in its unknowns (in which letters are used) one that is squared (or two), these terms are part of a quadratic function.
For a term to be quadratic it must be multiplied by itself (twice), for example:
a² + a + 1
We can see that it is a quadratic function and that its literal term is a while the quadratic term is a², i.e. a*a.
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A polynomial p(x)=x^(3)-3x^(2)+4x-12 can be expressed so that p(x)=q(x)*(x-1)+R What is the value of R ?
The value of R is -10.
The polynomial p(x)=x^(3)-3x^(2)+4x-12 can be expressed as p(x)=q(x)*(x-1)+R. To find the value of R, we need to divide the polynomial p(x) by (x-1) using synthetic division.
Set up the synthetic division by writing the coefficients of the polynomial p(x) in a row and placing the divisor (x-1) to the left of the row.
1 | 1 -3 4 -12
|_____________
Bring down the first coefficient (1) and multiply it by the divisor (1) to get 1. Place this value below the second coefficient (-3) and add them to get -2.
1 | 1 -3 4 -12
| 1
|_____________
1 -2
Multiply the new value (-2) by the divisor (1) to get -2. Place this value below the third coefficient (4) and add them to get 2.
1 | 1 -3 4 -12
| 1 -2
|_____________
1 -2 2
Multiply the new value (2) by the divisor (1) to get 2. Place this value below the fourth coefficient (-12) and add them to get -10.
1 | 1 -3 4 -12
| 1 -2 2
|_____________
1 -2 2 -10
The final value (-10) is the remainder, or the value of R.
Therefore, the value of R is -10.
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Find the area of each shaded region.
20. lan used 9½ cups of flour to make 1 batches of oatmeal cookies. One batch makes 18
cookies. If he follows the same recipe, about how many cookies can he make with 15 cups of
flour?
Answer:
To solve this problem, we can set up a proportion:
9.5 cups of flour / 18 cookies = 15 cups of flour / x cookies
To solve for x, we can cross-multiply:
9.5 cups of flour * x cookies = 18 cookies * 15 cups of flour
Dividing both sides by 9.5 cups of flour gives us:
x cookies = 18 cookies * 15 cups of flour / 9.5 cups of flour
x cookies ≈ 28.42
Since we can't make a fraction of a cookie, we'll round down to the nearest whole number. Therefore, Lan can make about 28 cookies with 15 cups of flour using the same recipe.
For the morning hours of 7-10 AM the mean number of arrivals at Dhaka Hardware is 5 customers per hour. What is the probability of a. 3 arrivals in an hour
b. at least 2 arrivals an hour
c. at most 1 arrival in an hour
d. No arrivals in an hour
The probability of A) 3 arrivals in an hour is approximately 0.1404, of B) at least 2 arrivals an hour is 0.918, of C) at most 1 arrival in an hour is 0.0821, and of D) no arrivals in an hour is 0.0067.
a. The probability of 3 arrivals in an hour can be calculated using the Poisson distribution formula: [tex]P(X = 3) = (e^{-5} * 5^3) / 3! = 0.1404[/tex]
b. The probability of at least 2 arrivals in an hour can be calculated by finding the complement of the probability of 0 or 1 arrival: [tex]P(X \geq 2) = 1 - P(X = 0) - P(X = 1) = 1 - e^{-5} * (5^0 / 0!) - e^{-5} * (5^1 / 1!) = 0.918[/tex]
c. The probability of at most 1 arrival in an hour can be calculated by adding the probabilities of 0 and 1 arrival: [tex]P(X \leq 1) = P(X = 0) + P(X = 1) = e^{-5} * (5^0 / 0!) + e^{-5} * (5^1 / 1!) = 0.0821[/tex]
d. The probability of no arrivals in an hour can be calculated by using the Poisson distribution formula: [tex]P(X = 0) = e^{-5} * (5^0 / 0!) = 0.0067[/tex]
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HELP ASAP
Find the missing angles in this rhombus
1
2
41°
3
measure of angle 1
measure of angle 2
measure of angle 3
By the properties of rhombuses, m∠1 = 90°, m∠2 = 41°, and m∠3 = 49°.
What is a rhombus?A quadrilateral with all equal sides is a rhombus.
Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.
A rhombus has 360° of interior angles total.
A rhombus's adjacent angles add up to 180°.
A rhombus's diagonals are perpendicular to one another and cut each other in half.
From the given figure and properties of the rhombus, m∠1 = 90°, As the diagonals bisect each other perpendicularly.
Now, The two diagonals have created 4 congruent right-angled triangles,
Therefore, m∠2 = 41°.
And m∠3 = 180° - (41° + 90°).
m∠3 = 49°.
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Estimate the solution of the linear system graphically and check the solution algebraically: A. A line graph showing 2 intersecting lines, the first line passes through the points (0, 5), (-1, 1), and (-3, -6) and the second line passes through the points (-3, 5), (-2, 3), (-1, 1), (0, -1), (1, -3), and (2, -5). B. A line graph showing 2 intersecting lines, the first line passes through the points (3, 4), (2, 1), (1, -2), and (0, -5) and the second line passes through the points (-5, 4), (-4, 3), (-3, 2), (-2, 1), (-1, 0), (0, -1), (1, -2), (2, -3), and (3, -4). C. A line graph showing 2 intersecting lines, the first line passes through the points (3, 4), (2, 1), (1, -2), (0, -5) and (-1, -8) and the second line passes through the points (5, 4), (4, 3), (3, 2), (2, 1), (1, 0), (0, -1), (-1, -2), (-2, -3), and (-3, -4). D. A line graph showing 2 intersecting lines, the first line passes through the points (2, 5), (1, 2), (0, -1), (-1, -4), and (-2, -7) and the second line passes through the points (-6, 5), (-5, 4), (-4, 3), (-3, 2), (-2, 1), (-1, 0), (0, -1), (1, -2), and (2, -3).
Using graph it is seen that the solution of the linear system is found as (-1, 1).
Explain about graphing linear system?It is as easy to graph two straight lines as it is a set of linear equations. The (x,y) arranged pair where it two lines intersect will be the answer when the lines being graphed (cross).When the crossing point has integer coordinates, the graphing method using graph paper may be helpful. However, it is less useful if the coordinates are still not integers. Use an algebraic optimization technique or get out your graphing calculator if it looks that its intersection point does not sit on the intersections of the grids on the graph paper.The points for the two intersecting lines are-
Red points: (0, 5), (-1, 1), and (-3, -6)
Green points: (-3, 5), (-2, 3), (-1, 1), (0, -1), (1, -3), and (2, -5).
Graph of there points are plotted.
Thus, it is seen that the solution of the linear system graphically is found as (-1, 1).
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The correct question is-
Estimate the solution of the linear system graphically and check the solution algebraically:
A line graph showing 2 intersecting lines, the first line passes through the points (0, 5), (-1, 1), and (-3, -6) and the second line passes through the points (-3, 5), (-2, 3), (-1, 1), (0, -1), (1, -3), and (2, -5).