SOLUTION: Two students used a graphing method to solve the system of equations. -4x+3y=5 2x+3y=-16 They used substitution to verify their solutions. Which student is correct? Explain

Question 1004519: Two students used a graphing method to solve the system of equations.
-4x+3y=5
2x+3y=-16
They used substitution to verify their solutions. Which student is correct? Explain the error.
STUDENT A:

STUDENT B

Thank you to anyone who can help! I sort of have an idea of how to solve this, but I'm not totally sure if it's correct.

Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The only solution is (x,y) = (-3.5, -3). Student A has the right idea.

-4x+3y = 5
-4(-3.5)+3(-3)=5
14-9 = 5
5 = 5 ... true

2x+3y=-16
2(-3.5)+3(-3) = -16
-7-9 = -16
-16 = -16 ... true

Both equations are true when (x,y) = (-3.5, -3), so the solution is confirmed.

======================================================

Student B used the wrong values for x and y

-4x+3y = 5
-4(4)+3(7) = 5
-16+21 = 5
5 = 5 ... true

2x+3y=-16
2(4)+3(7)=-16
8+21=-16
29 = -16 ... false

(x,y) = (4,7) makes the first equation true but the second equation false. Since it doesn't make both equations true, this means that (x,y) = (4,7) is NOT a solution.

Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
Both students checked incorrectly, although one of the students seems to have found the correct solution point.

Decide how you want to solve. Graphically?

Both equations are standard form, so you can find axis intercepts of each equation and graph each line using them.

Read the point of intersection shown on the graph.

A closer look:

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