Question

solve the following system of equations.
$x - 2y = 12$
$x + 5y = -16$
$x = \square$
$y = \square$

Explanation:

Step1: Isolate x from first equation

From \( x - 2y = 12 \), we get \( x = 12 + 2y \).

Step2: Substitute x into second equation

Substitute \( x = 12 + 2y \) into \( x + 5y = -16 \):
\( (12 + 2y) + 5y = -16 \)
Simplify: \( 12 + 7y = -16 \)
Subtract 12: \( 7y = -28 \)
Divide by 7: \( y = -4 \).

Step3: Find x using y

Substitute \( y = -4 \) into \( x = 12 + 2y \):
\( x = 12 + 2(-4) = 12 - 8 = 4 \).

Answer:

\( x = 4 \), \( y = -4 \)