Question

solve the following system of equations.
-6x + 7y = -12
2x - 5y = -12
x =

y =

Explanation:

Step1: Eliminate x, scale 2nd eq

Multiply the second equation by 3:
$$3(2x - 5y) = 3(-12) \implies 6x - 15y = -36$$

Step2: Add to 1st eq to eliminate x

Add the new equation to the first equation:
$$(-6x + 7y) + (6x - 15y) = -12 + (-36)$$
$$-8y = -48$$

Step3: Solve for y

Divide both sides by -8:
$$y = \frac{-48}{-8} = 6$$

Step4: Substitute y into 2nd eq

Plug $y=6$ into $2x - 5y = -12$:
$$2x - 5(6) = -12 \implies 2x - 30 = -12$$

Step5: Solve for x

Isolate x:
$$2x = -12 + 30 = 18 \implies x = \frac{18}{2} = 9$$

Answer:

$x = 9$
$y = 6$