Question

solve the following system of equations.
-8x + 3y = 17
-9x - 4y = -3
x =

y =

Explanation:

Step1: Eliminate y, scale equations

Multiply first eq by 4: $-32x + 12y = 68$
Multiply second eq by 3: $-27x - 12y = -9$

Step2: Add scaled equations

$$(-32x + 12y) + (-27x - 12y) = 68 + (-9)$$
$$-59x = 59$$

Step3: Solve for x

$$x = \frac{59}{-59} = -1$$

Step4: Substitute x into first equation

$$-8(-1) + 3y = 17$$
$$8 + 3y = 17$$

Step5: Solve for y

$$3y = 17 - 8 = 9$$
$$y = \frac{9}{3} = 3$$

Answer:

$x = -1$
$y = 3$