Question

solve the following system of equations.
$-9x - 2y = -2$
$-2x + 3y = 3$
$x = \square$
$y = \square$

Explanation:

Step1: Eliminate x via scaling equations

Multiply first equation by 2: $-18x - 4y = -4$
Multiply second equation by 9: $-18x + 27y = 27$

Step2: Subtract equations to solve for y

Subtract new first eq from new second eq:
$$(-18x + 27y) - (-18x - 4y) = 27 - (-4)$$
$$31y = 31$$
$$y = 1$$

Step3: Substitute y=1 into second equation

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

Step4: Solve for x

$$-2x = 3 - 3$$
$$-2x = 0$$
$$x = 0$$

Answer:

$x = 0$
$y = 1$