Question

solve the following system of equations.
-7x - 9y = 23
-8x + 3y = 13
x =

y =

Explanation:

Step1: Eliminate \( y \) by multiplying the second equation by 3

The second equation is \( -8x + 3y = 13 \). Multiply it by 3:
\( 3(-8x + 3y) = 3(13) \)
\( -24x + 9y = 39 \)

Step2: Add the new equation to the first equation

First equation: \( -7x - 9y = 23 \)
Add to \( -24x + 9y = 39 \):
\( (-7x - 9y) + (-24x + 9y) = 23 + 39 \)
Simplify: \( -31x = 62 \)

Step3: Solve for \( x \)

Divide both sides by \( -31 \):
\( x = \frac{62}{-31} = -2 \)

Step4: Substitute \( x = -2 \) into the second original equation to find \( y \)

Second equation: \( -8(-2) + 3y = 13 \)
Simplify: \( 16 + 3y = 13 \)
Subtract 16: \( 3y = 13 - 16 = -3 \)
Divide by 3: \( y = \frac{-3}{3} = -1 \)

Answer:

\( x = -2 \)
\( y = -1 \)