The system of linear equations will be 2x+3y=8, 4x+6y=15.
Which mathematical equation is the most challenging?
A mathematics issue have baffled the finest scientists in the world for decades. The Diophantine equation x3+y3+z3=k, where k is the sum of all of the numbers from 1 to 100, is sometimes referred to as the "sum of three cubes."
What is an equation's most basic form?
The lowest corresponding fraction of the integer is its simplest form. How to determine the simplest form: Look for shared components in the denominator and numerator. Verify if a fractional integer includes a prime number.
For example:
2x+3y=8
4x+6y=15
Part C:
Using the example above,
2x+3y=8
4x+6y=15
If we multiply the first equation by , we get:
4x+6y=16
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Question 16. Let A be an m×n matrix, X an n×r matrix, and B an m×r matrix. Show that AX =B if and only if Axj=bj, j=1,…,r
Axj = bj, j=1,…,r.
To show that AX = B if and only if Axj = bj, j=1,…,r, we can start by recognizing that AX is an m×r matrix and B is an m×r matrix. Since the dimensions of these two matrices are the same, they are equal if and only if each corresponding element is equal.
Therefore, we can conclude that AX = B if and only if each corresponding element of AX is equal to its corresponding element in B. Mathematically, this is expressed as Axj = bj, j=1,…,r.
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. For each situation below, state the transformation(s) that occur between
f(x) and g(x).
(please fill out the whole thing I need it by tomorrow)
The transformations that are occurring between each of the function are given as follows:
f(x) = 14(x - 3) + 1 and g(x) = 7(x + 2) + 1: vertical compression by a factor of 1/2 and shift left 5 units.
f(x) = 6(x + 2) - 3 and g(x) = 8(x - 3) + 6: vertical stretch by a factor of 4/3, shift right 5 units and shift up 9 units.
f(x) = 3(x - 1) + 2/3 and g(x) = 3(3 - x) - 2/3: reflection over the y-axis, shift left 2 units and shift up 4/3 units.
f(x) = 1/3(x + 2) - 4 and g(x) = 1/3(-x - 2) + 6: reflection over the y-axis and shift up 10 units.
f(x) = 4/3(x - 2/3) + 1/3 and g(x) = 2/3(2/3 - x) = reflection over the y-axis, shift down of 1/3 units and vertical stretch by a factor of 2.
What are transformations?The curve of the graph "moves to the left/right/up/down," "it expands or compresses," or "it reflects" when a function is changed.
The transformation rules are defined as follows:
x -> x + a: shift left a unit.
x -> x - a: shift right a unit.
y -> y + a: shift up a unit.
y -> y - a: shift down a unit.
y -> ky, k > 1: vertical stretching by k times.
Vertical compression by a factor of k is achieved by y -> ky, k 1, horizontal compression by a factor of k is achieved by x -> kx, k > 1, and vertical stretch by a factor of k is achieved by x -> kx, k 1.
x -> -x: reflection over the y-axis.
y -> -y: reflection over the x-axis.
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Ian’s mom sang him S songs. Then his sister sang him two times as many as his mom had. If Ian listened to nine songs in all, Ian's mom sang _____songs.
Ian’s mom sang him S songs. Then his sister sang him two times as many as his mom had. If Ian listened to nine songs in all, Ian's mom sanghim twIan’s mom sang him S songs. Then his sister sang him two times as many as his mom had. If Ian listened to nine songs in all, Ian's mom sango times as many as his mom had. If Ian listened to nine songs in all, Ian's mom sang _____songs.
Use Euclid's first book to prove what specific quadrilaterals are produced by non-perpendicular, unequal, non-bisecting diagonals.
Using the definition of a parallelogram in Euclid's first book, we can say that a non-perpendicular, unequal, non-bisecting diagonal produces either a trapezium or a rhombus if the opposite angles are equal, then it is a rhombus, and if the opposite angles are unequal, then it is a trapezium.
To use Euclid's first book to prove what specific quadrilaterals are produced by non-perpendicular, unequal, non-bisecting diagonals, start by considering Euclid's definitions of a parallelogram, a trapezium, and a rhombus.
In Euclid's first book, a parallelogram is defined as a quadrilateral which has two pairs of equal and parallel sides, while a trapezium is defined as a quadrilateral which has two pairs of opposite sides parallel, but with the other two sides unequal and non-parallel.
Finally, a rhombus is defined as a quadrilateral (parallelogram) which has all four sides equal, and with the opposite angles equal.
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Write the given expression as a single trigonometric function. tan(3pi/7) - tan(2pi/5)/ 1+tan(3pi/7) tan(2pi/5)
On sοlving the given trigοnοmetric expressiοn using the trigοnοmetric identity, we fοund that it is equal tο tan (π/35).
What is an expressiοn?Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne maths οperatiοn, and a statement. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn. A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expressiοn οr mathematical expressiοn.
There are twο sοrts οf expressiοns in mathematics: numerical expressiοns, which οnly cοntain numbers, and algebraic expressiοns, which alsο include variables. Expressiοns can be categοrised as arithmetic/numerical expressiοns, fractiοnal expressiοns, οr algebraic expressiοns depending οn the terms they cοntain.
The given trigοnοmetric expressiοn is:
[tex]\frac{tan (3\pi /7) - tan (2\pi /5)}{1+tan (3\pi /7) tan (2\pi /5)}[/tex]
tan (a-b) = sin(a-b) / cοs (a-b)
= (sin a cοs b - cοs a sin b) / (cοs a cοs b + sin a sin b)
Dividing the numeratοr and denοminatοr by (cοs a cοs b), we get,
tan (a-b) = (tan (a) - tan (b)) / (1+tan a tan b)
This expressiοn is similar tο the given expressiοn.
Cοmparing,
a = 3π/7
b = 2π/5
[tex]\frac{tan (3\pi /7) - tan (2\pi /5)}{1+tan (3\pi /7) tan (2\pi /5)}[/tex] = tan( 3π/7 - 2π/5) = tan (π/35)
Therefοre on solving the given trigonοmetric expression using the trigonοmetric identity, we found that it is equal tο tan (π/35).
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PLSSSS HELP IF YOU TURLY KNOW THISSS
Answer:
x = -6
Step-by-step explanation:
-4 + 2x = 4x+8
-4-8 = 4x - 2x
-12 = 2x
x = -6
Answer:
x = - 6
Step-by-step explanation:
Hope this helps! <33
Lenny and Lisa have obtained a 30-year, fixed rate mortgage for $675,250 with a 7. 25% interest rate. They purchased 3 points and their rate is now 6. 875%. Factoring in the cost of points, when is the break-even point on their mortgage?
Purchasing 3 points and reducing their interest rate, Lenny and Lisa will save 84,541.84 in interest over the life of the loan.
To calculate the break-even point on their mortgage, we need to determine how much Lenny and Lisa paid for the points and how much they save on their interest rate over the life of the loan.
First, we need to determine how much Lenny and Lisa paid for the points. One point is equal to 1% of the total loan amount, so 3 points is equal to 3% of 675,250:
3 points = 3% x 675,250 = 20,257.50
Next, we need to calculate how much Lenny and Lisa save on their interest rate by purchasing the points. Their original interest rate was 7.25%, but they were able to reduce it to 6.875% by purchasing 3 points. This means they save 0.375% on their interest rate.
To calculate how much they save over the life of the loan, we need to use an amortization schedule. An amortization schedule shows how much of each payment goes towards interest and how much goes towards principal, and it also shows the remaining balance on the loan after each payment.
Using an online mortgage calculator, we can generate an amortization schedule for Lenny and Lisa's loan. Based on this schedule, they will pay a total of 931,231.40 in interest over the life of the loan if they keep their original interest rate of 7.25%. If they reduce their interest rate to 6.875%, they will pay a total of 846,689.56 in interest over the life of the loan.
This means that by purchasing 3 points and reducing their interest rate, Lenny and Lisa will save 84,541.84 in interest over the life of the loan.
To determine the break-even point on their mortgage, we divide the cost of the points by the amount they save on their interest rate per year.
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Help please it would mean a lot
The number of pounds of peaches sold is given as follows:
65 pounds, option 2.
How to obtain the amount?The amount is obtained solving a system of equations, for which the variables are given as follows:
Variable x: pounds of apples.Variable y: pounds of peaches.She sold a total of 165 pounds, hence:
x + y = 165
x = 165 - y.
She made $337.50, hence:
1.75x + 2.5y = 337.50.
Replacing the first equation into the second, the value of y is obtained as follows:
1.75(165 - y) + 2.5y = 337.50
0.75y = 48.75
y = 48.75/0.75
y = 65 pounds.
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Does anyone know how to solve this
y=-2x^(2) + 12x - 15 ;x=3
Cause when I try it I get y=-27
but answer is supposed to be y=3 and x=3
Pls explain how
Answer: Order of operations
Step-by-step explanation:
Plug in 3 for x so...
y = -2(3)² + 12(3) - 15
Don't forget the order of operations, exponents go first
y = -2(9) + 12(3) - 15
Then multiply
y = -18 + 36 - 15
Simplify
y = 3
Admission to the museum is $8. Students receive a 30% discount. How much de
students pay? How much is the discount worth?
Answer:
The students would be paying a low amount of $5.60. The 30% discount takes off $2.40 of the original price, so the discount is worth $2.40
please help I have new clue what it is asking.
Answer:
110° and 215°
Step-by-step explanation:
the bearing of one point to another is the measure of the clockwise angle from the north line N at the point C to the point D , that is
(a)
bearing of D from C is 110° ( purple shaded angle )
(b)
the bearing of D from C is 215° ( blue shaded angle )
Consider the function f : R→R
given by f(x) = x^(4) - 32 x^(2)
Find the minimum and and maximum values (absolute) of f over the interval [3,5]. Provide the exact values. Minimum value a Maximum value.
The minimum value of f(x) over the interval [3,5] is -512 and the maximum value is 225.
To find the minimum and maximum values of the function f(x) = x^(4) - 32 x^(2) over the interval [3,5], we can use the following steps:
1. Find the first derivative of the function: f'(x) = 4x^(3) - 64x
2. Set the first derivative equal to zero to find the critical points: 4x^(3) - 64x = 0
3. Solve for x to find the critical points: x = 0, x = 4√2, x = -4√2
4. Check the value of the function at the critical points and at the endpoints of the interval to find the minimum and maximum values.
5. The minimum value occurs at x = 4√2, where f(4√2) = (4√2)^(4) - 32(4√2)^(2) = -512
6. The maximum value occurs at x = 5, where f(5) = 5^(4) - 32(5)^(2) = 225
7. Therefore, the minimum value is -512 and the maximum value is 225.
The least value of f(x) over the interval [3,5] is -512 and the largest value is 225.
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the function x^4 - 2x^3 - 6x^2 +22x - 15 has how many roots
write in complete sentences
By the fundamental theorem of algebra, it has exactly 4 complex roots, counting multiplicities.
What are Functions?A function is a mathematical rule that assigns a unique output value for each input value. It is a set of ordered pairs where the first element is the input and the second element is the output.
The given function is a polynomial of degree 4. Therefore, by the fundamental theorem of algebra, it has exactly 4 complex roots, counting multiplicities.
However, we do not know if these roots are all real or if some of them are complex. To determine this, we would need to use techniques such as factoring, synthetic division, or the quadratic formula to solve for the roots of the polynomial.
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Please scroll to the bottom of page for END of question.
(ix) (1 mark)
Answer:
(x) (1 mark)
Answer:
(xi) (1 mark)
Answer:
(xii) (1 mark)
Please choose one:
a)
b)
c)
d)
I apologize, but it seems that the question is incomplete or has not been properly formatted. Please provide the full question and any additional details or context so that I can accurately and effectively answer it. Thank you.
Alexandra buys a swing set online for $745.If shipping and handling are an additional 21% of the price,how much shipping and handling will Alexandra pay?
Answer:
$156.45
Step-by-step explanation:
Swing set $745
21/100 x $745 = 156.45
Please be meeeeee!!!
Answer:
answer is sus.
Step-by-step explanation:
sus is the correct answer to your problrm. hope this helps!
PLEASE HELP ME ITS DUE TODAY I will give brainlyist
The cone is composed of a half sphere and a triangular cone, the total volume would be 301.59 cubic centimeters.
What shapes compose the cone?This cone is composed of two shapes, these shapes are:
A triangular cone placed upside down A half-sphere which has been placed over the cone.What is the volume?The volume of the cone can be calculated using the following formula:
V=1/3hπr²
V= 1/3 10 π4²
V= 167.55 cm
The volume of the sphere can be calculated using the following formula:
V = 4/3 π r³ /
V = 4/3 π 4³/ 2
V = 268.08 / 2 = 134.04 cm
Total volume : 134.04 + 167.55 = 301.59 cubic centimeters
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Solve the syslem by either the addition mothod or the substitution method. y=2x-7 y=4x-21
Using the addition method the solution to the system is (x,y) = (14/3, 7/3) and using the substitution method the solution to the system is (x,y) = (7,7).
Using the addition method, we can rearrange the equations so that one of the variables cancels out:
y=2x-7 -> -2x + y = -7
y=4x-21 -> -4x + y = -21
Now, we can add the two equations together to eliminate the y variable:
-2x + y = -7
-4x + y = -21
______________
-6x = -28
Next, we can solve for x:
x = 28/6 = 14/3
Now, we can substitute this value of x back into one of the original equations to find y:
y = 2x - 7 = 2(14/3) - 7 = 28/3 - 21/3 = 7/3
So the solution to the system is (x,y) = (14/3, 7/3).
Using the substitution method, we can substitute one equation into the other to eliminate one of the variables. For example, we can substitute the first equation, y=2x-7, into the second equation, y=4x-21:
2x-7 = 4x-21
Next, we can rearrange the equation to solve for x:
2x = 14
x = 7
Now, we can substitute this value of x back into one of the original equations to find y:
y = 2x - 7 = 2(7) - 7 = 7
So the solution to the system is (x,y) = (7,7).
In conclusion, we can solve the system y=2x-7 and y=4x-21 using either the addition method or the substitution method to find the solution (x,y).
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Evaluate the function when x = 3.
f(x) = 5x + 2
A. -1/5
B. 1
C. 3
D. 7
Answer:
To evaluate the function when x = 3, we substitute 3 for x in the given function f(x) = 5x + 2:
f(3) = 5(3) + 2
f(3) = 15 + 2
f(3) = 17
Therefore, when x = 3, the value of the function f(x) = 5x + 2 is 17.
So, the correct answer is option D, 7 is incorrect because 5*3+2 = 17.
The Answers given are incorrect this is because the correct answer is 5.7
f(x) = 5x + 2
f(3)=5(3)+2
3f=15+2
3f=17
3f÷3=17÷3
f=5.66666666667
=5.7
Please answer this question
Answer:
14
Step-by-step explanation:
Help me fast its late and I gotta sleep this was due 6 minutes ago, I barely understand anything from this lesson and I don't got the best teacher so please help
Answer:
Step-by-step explanation:
Im not sure I can't see the picture.
Answer: Hence, the width of the path is 4 meters.
First we should find the area of the pool. Our width is 14 and our length is 18. In order to find the area, we must multiply these two numbers. 14 times 18 is 252. This means that the area of the pool is 252.
Since we know that one side of the pool is 18 and one side is 14, we can write out the equation below.
572= (18+2x)(14+2x)
The first thing we should do is combine like-terms.Our equation would now be as below.
x^2+16-80=0
Next we would take our quadratic equation- x=-b+-√b2-4ac/2a and fill it in with the numbers that we had in the first equation, our equation would be like below. A=1 B=16 C=-80
x=-16+-√16^2-4* 1 * -80 /2 * 1
When then simplify our equation leaving us with x=-16+-√16^2-4*1(-80)/2 * 1, which broken down is x=-16+-√+-24/2.
Lastly we must subtract and add to receive our two answers.
One side is 4 and the other is -20. Since the width of the walk cannot not be a negative number, we know that the width of the path is 4 meters.
Hence, the width of the path is 4 meters.
I hope this helped & Good Luck <3!!!
Solve the following rational equation: If no solution exists then state that. Show complete work. y/y−2y+ 4/y-3 = 4/ y2−5y+6
The answer: no real solutions to this equation
To solve the equation, we need to find a common denominator for all of the fractions on the left side of the equation. The common denominator will be (y-2)(y-3), so we will multiply each fraction by the appropriate factor to get the common denominator.
[tex]y/y -2y+ 4/y-3 = 4/ y2-5y+6[/tex]
[tex]y(y-3)/(y-2)(y-3) - 2y(y-2)/(y-2)(y-3) + 4(y-2)/(y-2)(y-3) = 4/(y-2)(y-3)[/tex]
Now we can combine the fractions on the left side of the equation:
[tex](y2-3y-2y2+4y+4y-8)/(y-2)(y-3) = 4/(y-2)(y-3)[/tex]
Simplifying the numerator on the left side gives us:
[tex](-y2+5y-8)/(y-2)(y-3) = 4/(y-2)(y-3)[/tex]
Now we can cross-multiply and simplify:
[tex](-y2+5y-8) = 4[/tex]
[tex]-y2+5y-12 = 0[/tex]
To solve this equation, we can use the quadratic formula:
[tex]y=\left(-5\pm \sqrt{52-4\left(-1\right)\left(-12\right)}\right)[/tex]
[tex]y=\left(-5\pm \sqrt{25-48}\right)[/tex]
[tex]y=\left(-5\pm \sqrt{-23}\right)[/tex]
Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, the answer is no solution.
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6 x 7-3 x 96 / 2+ 86 / 7 x 354 /21
The value of the expression is approximately -102.8571.
Why is the mathematical concept of the order of operations important?A set of guidelines known as the order of operations establishes the order in which mathematical operations should be carried out. Mathematical computations are carried out consistently and accurately by following the correct order of operations. Without a set order of operations, it would be possible for individuals to incorrectly and erroneously understand mathematical equations.
The given expression is:
6 x 7 - 3 x 96 / 2 + 86 / 7 x 354 / 21
= 42 - 288 / 2 + 86 / 49 x 354 / 21
= 42 - 144 + 4 x 354 / 21
= -102.8571
Hence, the value of the expression is approximately -102.8571.
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Heatrow airport in london england employs 80 chefs to prepare meals for international flight
9/5 x (4 x 1/6) please type the right answer
Answer:
Below
Step-by-step explanation:
9/5 X 4/1 X 1/6 = ( 9 x 4 x 1) / (5 x 1 x 6) = 36/30 = 1 6/30 = 1 1/5
Answer:
1 1/5
Step-by-step explanation:
Please help and just tell me the answers for each box I don’t need an explanation!!! 20 points
Answer:
(-2 . x) + (-2 . 5) = 4
-2x + -10 = 4
-2x = 4 + 10
-2x / -2 = 14/- 2
x = -7
All the best to you!
Dylan has two measuring jugs, A and B, which hold a combined volume of 800ml. Dulan fill jug A with water. He then fills jug B by pouring in water from jug A. After this, there is 200 ml of water remaining in jug A. Work out the volune of each measuring jug
Jug A has a vοlume οf 400 ml and jug B has a vοlume οf 400 ml.
What is the equatiοn in twο variables?An equatiοn in twο variables is an equatiοn that invοlves twο variables, typically x and y, and relates them with cοnstants and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.
Let's represent the vοlume οf jug A by x and the vοlume οf jug B by y.
We knοw that the cοmbined vοlume οf the twο jugs is 800 ml:
x + y = 800 (equatiοn 1)
We alsο knοw that after pοuring water frοm jug A tο jug B, there is 200 ml οf water remaining in jug A. This means that jug B cοntains x ml οf water:
y = x (equatiοn 2)
We can substitute equatiοn 2 intο equatiοn 1 tο eliminate y:
x + y = 800
x + x = 800
2x = 800
x = 400
Nοw that we knοw that the vοlume οf jug A is 400 ml, we can use equatiοn 2 tο find the vοlume οf jug B:
y = x
y = 400
Therefοre, the vοlume οf jug B is alsο 400 ml.
Hence, jug A has a vοlume οf 400 ml and jug B has a vοlume οf 400 ml.
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"Find the total price: Total bill: $45.65 Tip: 22% Tax: 5%"
Answer:
To find the total price, we need to add the tip and tax to the total bill amount.
First, we need to find the amount of the tip. To do this, we will multiply the total bill by 22% (or 0.22):
$45.65 x 0.22 = $10.04
This means the tip amount is $10.04.
Next, we need to find the amount of tax. To do this, we will multiply the total bill by 5% (or 0.05):
$45.65 x 0.05 = $2.28
This means the tax amount is $2.28.
Finally, we can find the total price by adding the total bill, tip, and tax together:
$45.65 + $10.04 + $2.28 = $57.97
Therefore, the total price is $57.97.
Write and solve an equation for the following situation in order for a ladder to reach a height of 10 feet it needs to be placed at a 75
If the ground already has an elevation of 15 degree. The degree that the ladder need to be set is 65.4 degrees.
What degree does the ladder need to be set?Angle at which the ladder is set from the horizontal = x.
Angle between the ladder and the ground = (75 - 15 + x) degrees
Using trigonometry, we can write the equation:
tan(75 - 15 + x) = 10 / L
where:
L= length of the ladder.
Simplifying the left-hand side using the trigonometric identity for the tangent of the difference of two angles, we get:
tan(60 + x) = 10 / L
Multiplying both sides by L, we get:
L * tan(60 + x) = 10
Dividing both sides by tan(60 + x), we get:
L = 10 / tan(60 + x)
Using a calculator, we can evaluate the right-hand side to be:
L = 10 / tan(60 + x) ≈ 5.768 / tan(x)
So, the equation we need to solve for x is:
5.768 / tan(x) = L
Substituting the value of L obtained from the previous problem, we get:
5.768 / tan(x) = 2.68
Multiplying both sides by tan(x), we get:
5.768 = 2.68 tan(x)
Dividing both sides by 2.68, we get:
tan(x) ≈ 2.153
Using a calculator, we can find the value of x that satisfies this equation by taking the inverse tangent (tan^-1) of both sides:
x ≈ 65.4 degrees
Therefore, the ladder needs to be set at an angle of approximately 65.4 degrees from the horizontal in order to reach a height of 10 feet when the ground already has an elevation of 15 degrees and the ladder is placed at a 75-degree angle with the ground.
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The complete question is:
Write and solve an equation for the following situation in order for a ladder to reach a height of 10 feet it needs to be placed at a 75 degree to the ground . The ground already has an elevation of 15 degree. What degree does the ladder need to be set?
The linear system shown is equivalent
The linear system shown is "inconsistent" in nature.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
The given figure is represented linear system represents two parallel lines.
Now, the solution set of the two system of equations could be find by finding their points of intersection.
And when the lines do not intersect then it is said the linear system of the two lines do not have any solution.
Now, we have been given two parallel lines and parallel lines never intersect each other. thus the solution set of both the system of equations represented by these parallel lines is an empty set.
And when the system of linear equation has no solution , then the system is said to be inconsistent.
Hence, The linear system shown is "inconsistent" in nature.
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The complete question is;
The linear system shown is _____.
independent
equivalent
inconsistent