Question

solve the following system of equations.
$-4x+5y=-12$
$5x-2y=15$
$x=\square$
$y=\square$

Explanation:

Step1: Eliminate y, scale equations

Multiply first eq by 2: $-8x + 10y = -24$
Multiply second eq by 5: $25x - 10y = 75$

Step2: Add scaled equations

$$(-8x + 10y) + (25x - 10y) = -24 + 75$$
$$17x = 51$$

Step3: Solve for x

$$x = \frac{51}{17} = 3$$

Step4: Substitute x=3 into second eq

$$5(3) - 2y = 15$$
$$15 - 2y = 15$$

Step5: Solve for y

$$-2y = 15 - 15 = 0$$
$$y = 0$$

Answer:

$x = 3$
$y = 0$