Question

-5x - 3y = 18
2x - 7y = 1

Explanation:

Step1: Eliminate x via scaling equations

Multiply first eq by 2: $-10x - 6y = 36$
Multiply second eq by 5: $10x - 35y = 5$

Step2: Add equations to solve for y

Add the two new equations:
$$(-10x - 6y) + (10x - 35y) = 36 + 5$$
$$-41y = 41$$
$$y = -1$$

Step3: Substitute y into second equation

Substitute $y=-1$ into $2x - 7y = 1$:
$$2x - 7(-1) = 1$$
$$2x + 7 = 1$$

Step4: Solve for x

Isolate x:
$$2x = 1 - 7$$
$$2x = -6$$
$$x = -3$$

Answer:

$x=-3$, $y=-1$