Question

Here are Janet's steps for solving the system below by eliminating x.

2x + 3y = -1 5x + 8y = 0
Step One: Multiply the first equation by 5. 10x + 15y = -5
Step Two: Multiply the second equation by -2. -10x - 16y = 0
Step Three: Add the two equations. y = -5 Step
Four: Substitute y back into the first equation. 2x + 3(-5) = -1
Step Five: Solve for x. 2x - 15 = -1 2x = 14 x = 7 Is she correct? Justify your answer. If incorrect, describe the error.

Answer 1

2x + 3y = -1.....(5)
5x + 8y = 0.....(-2)
-----------------------
10x + 15y = -5
-10x - 16y = 0
-----------------------add
-y = -5
y = 5 <=====this is where Janet messed up

2x + 3y = -1
2x + 3(5) = -1
2x + 15 = -1
2x = -1-15
2x = -16
x = -16/2
x = - 8

solution is : (-8,5)