Question

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

Explanation:

Step1: Label the equations

Let Equation 1: $-5x + 5y = -25$
Let Equation 2: $3x + 2y = 10$

Step2: Simplify Equation 1

Divide Equation 1 by 5:
$\frac{-5x}{5} + \frac{5y}{5} = \frac{-25}{5}$
$-x + y = -5$
Rearrange to isolate $y$: $y = x - 5$

Step3: Substitute $y$ into Equation 2

Substitute $y = x - 5$ into $3x + 2y = 10$:
$3x + 2(x - 5) = 10$

Step4: Solve for $x$

Expand and simplify:
$3x + 2x - 10 = 10$
$5x - 10 = 10$
$5x = 10 + 10$
$5x = 20$
$x = \frac{20}{5} = 4$

Step5: Solve for $y$

Substitute $x=4$ into $y = x - 5$:
$y = 4 - 5 = -1$

Answer:

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