Question

solve the following system of equations.
$-6x+5y=11$
$3x-8y=22$
$x=\square$
$y=\square$

Explanation:

Step1: Eliminate x, scale 2nd eq

Multiply the second equation by 2:
$$2\times(3x - 8y) = 2\times22 \implies 6x - 16y = 44$$

Step2: Add to 1st eq, solve for y

Add the new equation to the first equation:
$$(-6x + 5y) + (6x - 16y) = 11 + 44$$
$$-11y = 55$$
$$y = \frac{55}{-11} = -5$$

Step3: Substitute y into 2nd eq

Plug $y=-5$ into $3x - 8y = 22$:
$$3x - 8\times(-5) = 22$$
$$3x + 40 = 22$$

Step4: Solve for x

Isolate x and calculate:
$$3x = 22 - 40 = -18$$
$$x = \frac{-18}{3} = -6$$

Answer:

$x = -6$
$y = -5$