Question

1. polly took a quiz on solving systems of linear equations. she was not sure how she did on two of the harder problems when she turned in the quiz. later, her friend told her she should have checked her answers. did polly answer the questions correctly? explain your reasoning.

a.
$y = 4x - 1$
$2x - y = -13$
pollys solution $(-2, -9)$
b.
$3x + 6y = 15$
$-2x + 3y = -3$
pollys solution $(3, 1)$

Explanation:

Step1: Check Part a: Substitute $x=-2, y=-9$ into $y=4x-1$

Substitute values: $-9 = 4(-2) - 1$
Calculate right-hand side: $4(-2)-1=-8-1=-9$

Step2: Check Part a: Substitute into $2x-y=-13$

Substitute values: $2(-2)-(-9) = -13$
Calculate left-hand side: $-4 + 9 = 5$

Step3: Check Part b: Substitute $x=3, y=1$ into $3x+6y=15$

Substitute values: $3(3)+6(1)=15$
Calculate left-hand side: $9+6=15$

Step4: Check Part b: Substitute into $-2x+3y=-3$

Substitute values: $-2(3)+3(1)=-3$
Calculate left-hand side: $-6+3=-3$

Answer:

a. Polly's solution $(-2, -9)$ is incorrect. While it satisfies $y=4x-1$, it does not satisfy $2x-y=-13$ (the left-hand side equals 5, not -13).
b. Polly's solution $(3, 1)$ is correct. It satisfies both $3x+6y=15$ and $-2x+3y=-3$.