Systems of Linear Equations Unit Test

Question

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Question
Solve the following system of linear equations by graphing. Graph on your own piece of paper. In your submitted answer, describe what the graph looks like and what this tells you about the solution to the system of linear equations.

y=x+3

−4x+4y=28

Answer 1

To solve the system of linear equations by graphing, we first need to rearrange the second equation to solve for y:

-4x + 4y = 28
4y = 4x + 28
y = x + 7

Now we have the two equations:
y = x + 3
y = x + 7

When we graph these two equations, we can see that they are parallel lines with different y-intercepts. The first line, y = x + 3, has a y-intercept of 3 and a slope of 1. The second line, y = x + 7, has a y-intercept of 7 and a slope of 1. Since these lines are parallel, they will never intersect.

Therefore, the system of linear equations does not have a solution.