Question

solve the following system of equations.
-5x - 3y = 18
-8x - 7y = 9
x =

y =

Explanation:

Step1: Eliminate a variable (e.g., y)

Multiply the first equation by 7 and the second by 3 to make coefficients of y equal:
First equation: \( -5x - 3y = 18 \) → \( -35x - 21y = 126 \)
Second equation: \( -8x - 7y = 9 \) → \( -24x - 21y = 27 \)

Step2: Subtract the two new equations

\( (-35x - 21y) - (-24x - 21y) = 126 - 27 \)
Simplify: \( -35x + 24x = 99 \) → \( -11x = 99 \)

Step3: Solve for x

Divide both sides by -11: \( x = \frac{99}{-11} = -9 \)

Step4: Substitute x = -9 into first equation

\( -5(-9) - 3y = 18 \) → \( 45 - 3y = 18 \)

Step5: Solve for y

Subtract 45: \( -3y = 18 - 45 = -27 \)
Divide by -3: \( y = \frac{-27}{-3} = 9 \)

Answer:

\( x = -9 \)
\( y = 9 \)