Can somebody give me an review over how to solve systems of equations by substitution and elimination? PLEASE HELP I forgot how to do it and my Algebra EOC is TOMORROW!! I provided an example question and I need LONG ACCURATE and HELPFUL explanations, not a one sentence response (or I will report you). PLEASE HELP ME!!!
Answers
Answer:
Price per large envelope = $1.42 (option A)
Price of each postcard = $0.35 (not asked for in this specific question)
Step-by-step process for solution given below
Step-by-step explanation:
The first thing to do for this problem and other similar problems is to set up the system of linear equations to be solved
We start with the unknowns and provide variable names for these unknowns
There are two unknowns here - the cost of each postcard and the cost of each large envelope
Let
x = cost of one postcard
y = cost of one large envelope
Customer 1 bought 14 postcards(cost = 14x) and 5 envelops(cost = 5y) for a total cost of $12
We can set up this as an equation:
12x + 5y = 12 ............ [1]
Customer 2 bought 10 postcards(cost = 10x) and 15 envelops(cost = 15y) for a total cost of $24.80
This translates to the following equation:
10x + 15y = 24.80 .... [2]
Let's re-write these equations one below the other for easier solution:
[tex]\begin{amatrix}14x+5y=12\dots[1]\\ 10x+15y=24.8\dots[2]\end{amatrix}[/tex]
Solving by substitution:
From any one of the above equations, express one variable in terms of the other variable and substitute for that variable in the other equation to solve.
Take equation [1]
[tex]14x+5y=12[/tex]
Let's express x in terms of y.
Move 5y to the right:
[tex]14x=12-5y[/tex]
[tex]x =\dfrac{12-5y}{14}[/tex]
Use this expression in y for x in equation [2]
[tex]10x + 15y = 24.8\\\\\implies 10 \cdot \dfrac{12-5y}{14}+15y=24.8\\\\\implies \dfrac{\left(12-5y\right)\cdot \:10}{14} + 15y = 24.8\\\\\implies \dfrac{\left(12-5y\right)\cdot \:10}{14} + 15y = 24.8\\\\[/tex]
Multiply throughout by 14:
[tex]14 \cdot \dfrac{\left(12-5y\right)\cdot \:10}{14} + 14\cdot 15y = 14 \cdot 24.8\\\\(12-5y)10 + 210y = 347.2\\\\120 - 50y + 210y = 347.2\\\\120 + 160y = 347.2\\\\160y = 347.2- 120\\\\160y = 227.2\\\\y = \dfrac{227.2}{160}\\\\y = 1.42[/tex]
Substitute y = 1.42 in equation [tex]x=\dfrac{12-5y}{14}[/tex]
[tex]x=\dfrac{12-5\cdot \:1.42}{14}\\\\x = 0.35\\\\[/tex]
So the cost of each large envelope was $1.42 and cost of each postcard was $0.35
Answer is option A
Solve by elimination
The idea here is to get the coefficients of one of the variables the same in both equations by multiplying / dividing one or both of the equations by some factor and then add/subtract to isolate the other variable and solve
For equations 1 and 2 do the following
Subtract the equations:
[tex]70x+105y=173.6\\-\\70x+25y=\;\;\;\;\;60\\\\[/tex]
-------------------------------
[tex]80y=113.6[/tex]
y = 113.6/80 = 1.42 as before
Substitute for y in equation 1 and solve for x
14x + 5y = 12 => 14x + 5(1.42) = 12
=> 14x + 7.1 = 12
=> 14x = 12 - 7.1
=> 14x = 4.9
=> x = 4.9/14 = 0.35 as before
I personally prefer solving by elimination since solving by substitution involves heavy duty fractional expressions
Related Questions
Anyone knows the answer???
Answers
Answer:b
Step-by-step explanation:
Answer:
#3 points are
(-4, 2)
(4, 2)
(-4, -2)
(4, 0)
#4 scale factor = 1/4
#5 scale factor = 1/2
Step-by-step explanation:
#3
take the given points and multiply the x and y by 2/3
#4 take any point and compare it to a similar point on the dilated graph. for example, you take a point from the original graph (-2, 4) and a point from the dilated graph (-1/2, 1) since you multiply -2 by 1/4 to get -1/2, that is your scale factor.
#5 same as #4 but with different points
Of 100 students surveyed, 42 own a dog, 34 own a cat, 15 own a dog and cat, and 9 own neither a dog nor a cat. Based upon the results, how many of the next 20 students surveyed would you expect to own a dog and cat. Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
PLEASE HELP!!!!
Answers
Answer: 3
Step-by-step explanation: 15% of the people surveyed had both a cat and a dog, so you would find 15% of 20. Find 15% of 20 by doing 20 x .15
What is the area of Z?
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Answer:
t = 5 kilometers
Step-by-step explanation:
From the given figure,
Perimeter = 18 kilometers
Now, the formula for perimeter of a rectangle = 2(l + b)
Where,
'l' is the length of the rectangle
and
'b' is the breadth of the rectangle.
Since length is the longest side of a rectangle, therefore from the given figure
=> l = t kilometers
and
=> b = 4 kilometers
Substituting values in the formula,
18 = 2(t + 4)
=> 18/2 = t + 4
=> 9 = t + 4
=> 9 - 4 = t
=> t = 5 kilometers
Answer:
5 km
Step-by-step explanation:
We know that the perimeter of this rectangle is 18km.
We also know that 1 side is 4km.
Given the perimeter formula:
[tex]P=2(l+w)[/tex]
We can substitute our given values:
18=2(4+w)
Solve the right side
18=8+2w
subtract 8 from both sides
10=2w
divide both sides by 2
5=w
This means that z, the width, is 5 km.
Hope this helps!
help me please i need to answer this
Answers
b. 59
c. m
I think c. is m but the rest of the answers are correct. Can i get brainliest?
a. 24
b. 35
c. m
Answer quick quickest gets brainliest
For each of the shapes below, state if its a regular polygon, irregular polygon or neither
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Answer:
A and B - irregular, C - neither, D and E - regular----------------------------
Regular polygon has congruent sides and angles.
Irregular polygon has different sides and angles.
According to markings on figures and properties we can state:
A) Irregular 6-sided polygon, irregular hexagon;B) Irregular 4-sided polygon, isosceles trapezoid;C) Neither, not a polygon as no sides or angles, it is a circle;D) Regular 3-sided polygon, equilateral triangle;E) Regular 8-sided polygon, octagon..........................
Answers
Answer: 10
Step-by-step explanation:
20*6*8=960
960/(12*8)=10
Answer:
10
Step-by-step explanation: volume=l*w*h 20*6*8=960 12*8*10=960
PLEASE HELP
Can someone please help, my teacher wants this done a certain way and I don't know how to do it.
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Thank you for your help! :D
Answers
The number of times Maria drove the car on day 4 is 7 times.
How many times did Maria drive her car on day 4?A line graph is a graph that connects different data points on a graph using a straight line. A line graph is made up of a x-axis and a y-axis. In the line graph given, the number of days is on the x-axis and the number of times the car was driven is on the y-axis. A line graph is used to show quantitative data. Line graphs are used to visualise data.
In order to determine the number of times Maria drove the car on day 4, locate where day 4 is on the x-axis. Then trace 4 upward toward a data point. When the data point is located, trace it to the y-axis. When day 4 is traced to the y-axis, the value gotten is 7.
To learn more about line graphs, please check: brainly.com/question/27252279
Answer:
She drove her car 7 times on day 4.
Step-by-step explanation:
The left column is how many times she drove her car and on day 4, the yellow dot is on line 7.
Solve: 8/12=_/15, multiply 8/12 with a number that will give you _/15
Answers
8/12= x/15
8/12 simplified is 2/3
2/3= x/15
15 divided by 3 = 5
5 (2) = 10
10/15= 0.66667
Kyle has a storage box that is 2 ft. long, 3 ft. high, and has a volume of [tex]12ft^{3}[/tex]
Myla has a storage box that is 4 ft. high, 2 ft. long, and has a volume of [tex]16ft^{3}[/tex]
What are the widths of Kyle and Myla's boxes? Explain how you know.
help please! and please have easy explanation that's easy to understand :))
Answers
Answer:
OK so, volume= length x width x height
so, if the length of kyles box is 2, and his height is 3, but the volume is 12, then the width would be 2.
2 x 2 x 3=12
however, for myla, if her box is, 2 feet long and 4 feet high, but the volume is 16, then, her width is also 2.
2 x 2 x 4= 16
a way to look at this is, in the problem you are given the height and length, so, if its length times width times height, take your given length and multiply it by a number that will make it equal your given volume.
for example, let q=width, let m=height, and let j=length, p=volume, h=random variable.
j (x) h (x) m=p
its your job to find h.
hope this helps!
Step-by-step explanation:
which statement is true?
Answers
Answer:
I believe the answer is B.
Step-by-step explanation:
Question 8!!
Total area= area of rhombus + area of triangle
Answers
Answer:
total area of the given figure is 126
step by step guide:
1) 14×6+1/2×14×6
2) 84+42
3) =126
Help with number 4 please
Answers
Please help will give brainlest and special thanks
Answers
Answer:
30
Step-by-step explanation:
3x+ 10= 100
-10 -10
3x=90
divide both sides by 3 nd you get 30
At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer mustard on a hot dog?
Group of answer choices
900
2,000
2,100
4,000
Answers
Answer:
I haven't done anything like this for many years, but i think the answer is 900
Step-by-step explanation:
5000/ 150 = 33.33333333
33.3333333 X 27 = 900
Again, I haven't done this in forever, but I'm 99% sure it is 900. :)
27/150= 0.18
so 18% of the 150 people like mustard
then 0.18 x 5000= 900
meaning it’d be estimated around 900
Angelica can ride her bike 30 miles in five hours. At this rate, how many miles will angelica ride in 3 hours?
Answers
Explanation:
30/5=6
6*3=18
Therefore, she can ride approximately 18 miles in 3 hours.
"Pure mathematics is, in its way, the poetry of logical ideas" -Albert Einstein
A waitress sold 15 ribeye steak dinners and 28 grilled salmon dinners, totaling $551.97 on a particular day. Another day she sold 24 ribeye steak dinners and 14 grilled salmon dinners, totaling $581.91. How much did each type of dinner cost?
Answers
Answer:
Ribeye (ea) = $18.54
Salmon (ea) = $9.78
Step-by-step explanation:
x is the price for each ribeye steak
y is the price for each grilled salmon
15x + 28y = $551.97 (a)
24x + 14y = $581.91 (b) -----(x2)------> 48x + 28y = 1163.82 (c)
Subtract c with a
48x + 28y = 1163.82 (c)
15x + 28y = $551.97 (a)
=================== -
33x = 611.85
x = 18.54
Put the value of x into a
15 · 18.54 + 28y = 551.97
278.1 +28y = 551.97
28y = 273.87
y = 9.78
In conclusion, the price of 1 ribeye is $18.54, and the price of 1 salmon is $9.78.
Multiply. (x + 5)(2x - 6)
Answers
Answer: 2x2+4x−30
Step-by-step explanation:
Answer: D) 2x² + 4x - 30. Step-by-step explanation: Follow the FOIL method: FOIL = First. Outside. Inside. Last ...and is the order you multiply to solve
Step-by-step explanation:
Help me solve question 2; both parts.
Answers
Please help with this one too! Thanks a bunch!♡
Answers
7x-2+4x+6=180
11x+4=180
11x=176
176/11
x=16
Question is in the picture
Answers
Please help will give brainlest and special thanks
Answers
Answer:
To find the x-intercept, substitute in
0 for y
and solve for x. To find the y-intercept, substitute in
0 for x
and solve for y.
x-intercept(s): (−5,0)
y-intercept(s): (0,10)
Step-by-step explanation:
90 30 + 50 +(2x+10)=90
HELP PLEASE I DONT KNOW ANYTHING
Answers
Answer: A=2cm
Step-by-step explanation:
All the sides of a regular hexagon are equal. SO PQ is the same as MN
Answer: It's A) 2 cm
Step-by-step explanation: All the sides are the same length.
Good luck!
A diamond merchant received a shipment of 4 ⅔ pounds of diamonds. She divided the diamonds into 6 equal lots and sold them to jewelers for making rings and necklaces. What was the weight of the diamonds in each lot?
Answers
Answer:7/9 of a pound in each lot
Step-by-step explanation:4 2/3 = 14/3
14/3 divided by 6 will give us 14/18 which simplifies to 7/9
HELPPPPPP PLSSS DUE TMRW
Answers
Answer:
13
13
Step-by-step explanation:
-7+6= 7+6= 13
-7+6= 7+6= 13
a) work: you have to solve -7+6=-1.
it’s in those brackets so you have to change it to positive
b) -7 changed to positive 7. 7+6=13
Of course, not all numbers are perfect squares. Complete the table by indicating whether the numerical value in each equation is a perfect square. If it isn’t a perfect square, indicate which perfect squares it is between.
Answers
Answer:
16,49 and 121 are perfect squares
Step-by-step explanation:
hope it helps :)
The tape diagram represents an equation. Write an equation to represent the image.
Answers
Answer: 6t = 9
Step-by-step explanation:
What is visually explicable is that the 2 tape diagrams are equal.
One tape diagram equals 9, one is divided into 6 equal parts, each equals t.
6t's make up a diagram that is equal to a diagram equal to 9.
therefore 6t=9
ILL GIVE BRAINLIEST WORTH 69 POINTS
Use the graph to answer the question. Graph of polygon ABCD with vertices at 1 comma negative 1, 3 comma negative 5, 7 comma negative 5, 5 comma negative 1. A second polygon A prime B prime C prime D prime with vertices at 1 comma negative 6, 3 comma negative 10, 7 comma negative 10, 5 comma negative 6. Determine the translation used to create the image. 5 units down 5 units up 1 unit down 1 unit up
Answers
Answer:
The translation used to create the image from polygon ABCD to polygon A' B' C' D' is 5 units down.
Step-by-step explanation:
You can see this by observing that all of the y-coordinates in A' B' C' D' are 5 units less than their corresponding y-coordinates in ABCD. Specifically, the y-coordinates of the vertices in ABCD are (-1, -5, -5, -1), and the y-coordinates of the vertices in A' B' C' D' are (-6, -10, -10, -6).
Therefore, the vertical shift or translation used to create the image is 5 units down.
Answer:
5 units down.
Step-by-step explanation:
To solve this question, we need to compare the coordinates of the corresponding vertices of the two polygons and see how they change. A translation is a type of transformation that slides a figure by a certain distance and direction without changing its size or shape. The rule of a translation can be written as (x, y) -> (x + h, y + k), where h and k are the horizontal and vertical shifts, we can see that:
A (1, -1) maps to A’ (1, -6), which means x stays the same and y decreases by 5.B (3, -5) maps to B’ (3, -10), which means x stays the same and y decreases by 5.C (7, -5) maps to C’ (7, -10), which means x stays the same and y decreases by 5.D (5, -1) maps to D’ (5, -6), which means x stays the same and y decreases by 5.We can see that all the vertices have the same change in their coordinates: x stays the same and y decreases by 5. This means that the translation used to create the image is 5 units down. The rule of this translation can be written as (x, y) -> (x, y - 5). Therefore, the answer is 5 units down.
What is the scale factor from the large triangle to the small triangle?
A. 1/2
B. 2/3
C. 1/3
D. 3/4
Answers
The rule is x→y=−2x. c Can you mark all the points that fit the rule on a coordinate plane?
Answers
Step-by-step explanation:
Y=0,-2,2
X=-1,0,1
Since x represent y = - 2x
The points that fit the rule on a coordinate plane are (0, 0), (1, -2), (2, -4) and (3, -6)
Selecting the points that fit the rule on a coordinate plane?From the question, we have the following parameters that can be used in our computation:
Rule: x→y=−2x
Express properly
So, we have the following representation
Rule: x → y = −2x
As an equation, we have
y = -2x
Next, we set values for x and calculate the value of y
Using the above as a guide, we have the following:
x : 0 → y = −2(0) = 0
x : 1 → y = −2(1) = -2
x : 2 → y = −2(2) = -4
x : 3 → y = −2(3) = -6
So, the points that fit the rule on a coordinate plane are (0, 0), (1, -2), (2, -4) and (3, -6)
Read more about linear relation at
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