Question

Use substitution to determine which system is represented by the graph.

Answer 1

Answer:

2x + 4y = 28

-2y = x + 28

Step-by-step explanation:

Looking at the graph, we can see that the lines do not intersect. Therefore, they do not have a shared solution. We need to find the system of equations that does not have a solution.

1) Let's try to solve the third system given (counting from the top). To solve with the substitution method, we need to isolate one variable in one of the equations. I chose to isolate y in -2y = x + 28:

$-2y = x + 28\\y = \frac{-1}{2}x -14$

2) Now that we've isolated the y in that equation, substitute what y equals in that equation for the y in the other equation. So, substitute $\frac{-1}{2}x-14$ for y in 2x + 4y = 28 and simplify:

$2x + 4(\frac{-1}{2}x - 14) = 28\\2x - 2x- 64 = 28\\-64 = 28$

In a normal situation, the x's would not cancel out, and we would be able to isolate x to get the x-value of the solution. However, in this case, they have, and we ended up with a false statement, as -64 does not equal 28. Whenever this happens, it means the system does not have a solution. Therefore, the third option would represent the system in the graph.