Question

-5x + 5y = -25; 3x + 2y = 10

Explanation:

Step1: Eliminate one variable (x)

Multiply first equation by 5: $5(-5x + 5y) = 5(-25) \implies -25x + 25y = -125$
Multiply second equation by 5: $5(3x + 2y) = 5(10) \implies 15x + 10y = 50$
Wait, correct scaling: Multiply first eq by 3, second by 5:
$3(-5x + 5y) = 3(-25) \implies -15x + 15y = -75$
$5(3x + 2y) = 5(10) \implies 15x + 10y = 50$
Add the two new equations:
$(-15x + 15y) + (15x + 10y) = -75 + 50$
$25y = -25$

Step2: Solve for y

$\frac{25y}{25} = \frac{-25}{25} \implies y = -1$

Step3: Substitute y into second equation

$3x + 2(-1) = 10$
$3x - 2 = 10$

Step4: Solve for x

$3x = 10 + 2 = 12$
$x = \frac{12}{3} = 4$

Answer:

$x = 4$, $y = -1$