This quiz challenges you to use a combination of algebraic (equation-based) solution methods and graphical solution methods. Please make sure that you only use the graphing tools included inside the quiz. If there is no graphing tool associated with a question, you should look for a solution that uses the equations and other information to find an answer.
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Question 1
1.
Which of the following (x,y) pairs is a solution to the system of equations?
Remember, a solution to a system of equations is a set of variable values that makes all the equations in the system true "simultaneously".
y=3x-17
y=\frac{2}{7}x+\frac{24}{7}
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Question 2
2.
Use the graphing tool to find the solution to the system of equations. Write your answer in the "show your work" section. Make sure your answer is in the form of an (x,y) value pair. You may provide an approximate answer rounded to the nearest hundredth.
y=\frac{4}{5}x-33
y=-2x+25
info
We have released a new and improved Graphing question type! Students will no longer be able to answer this question.
1 point
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Question 3
3.
What is the solution to the system of equations below? Make sure your answer is in the form of an (x,y) value pair.
y+\frac{7}{3}=\frac{3}{7}(x+3)
y+\frac{7}{3}=\frac{3}{13}(x+3)
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Question 4
4.
Describe the size of the solution set to the following system of equations. How many different (x,y) value pairs will make all these equations true at the same time? Explain your answer (you may write in the "show your work" section).
y=-2x+4
y=4x-4
y=-\frac{2}{9}x-2
info
We have released a new and improved Graphing question type! Students will no longer be able to answer this question.
1 point
1
Question 5
5.
Two architects are designing a house, but they are arguing about how big the large, rectangular living room should be.
Architect 1
The first architect thinks the room should be exactly 1.75 times as long as it is wide. She thinks this will make the shape of the room most convenient for furniture and most comfortable to be in. She creates a formula where you input how wide the room will be, and it spits out an answer saying how long the room will have to be.
\ell=f_{1}(w)=1.75w
Architect 2
The second architect disagrees. He thinks Architect 1’s method makes for difficult rooms to build, since you could have a room that’s got strange fractions of a foot. He uses a different formula where he multiplies the width by 1.5 and then just adds 5 more feet.
Obviously, the two architects disagree about how the length and width of the room should be related to each other. But, can you design a room that makes both architects happy? Explain why or why not. If a compromise is possible, what should the dimensions be?