Question

what is the solution to the system of equations?
-2x + y = -5
3x - 2y = 12
a (3, 1)
b (6, 3)
c (2, -9)
d (-2, -3)
e no solution

Explanation:

Step1: Isolate y from first equation

From $-2x + y = -5$, rearrange to get $y = 2x - 5$.

Step2: Substitute y into second equation

Substitute $y = 2x - 5$ into $3x - 2y = 12$:
$3x - 2(2x - 5) = 12$
Expand: $3x - 4x + 10 = 12$
Simplify: $-x + 10 = 12$

Step3: Solve for x

Rearrange to find $x$:
$-x = 12 - 10$
$-x = 2$
$x = -2$

Step4: Find y using x value

Substitute $x = -2$ into $y = 2x - 5$:
$y = 2(-2) - 5 = -4 - 5 = -9$

Step5: Verify solution

Check $(-2, -9)$ in $3x - 2y = 12$:
$3(-2) - 2(-9) = -6 + 18 = 12$, which matches.

Answer:

C. (-2, -9)