Question

question
find the solution of the system of equations.

$12x + 8y = -12$
$-2x - 2y = -4$

Explanation:

Step1: Simplify the second equation

Divide the second equation \(-2x - 2y = -4\) by \(-2\) to get \(x + y = 2\), which can be rewritten as \(x = 2 - y\).

Step2: Substitute \(x\) into the first equation

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

$$\begin{align*} 12(2 - y) + 8y&=-12\\ 24 - 12y + 8y&=-12\\ 24 - 4y&=-12 \end{align*}$$

\]

Step3: Solve for \(y\)

Subtract 24 from both sides: \(-4y = -12 - 24 = -36\)
Divide by \(-4\): \(y = \frac{-36}{-4} = 9\)

Step4: Solve for \(x\)

Substitute \(y = 9\) into \(x = 2 - y\): \(x = 2 - 9 = -7\)

Answer:

The solution of the system is \(x = -7\), \(y = 9\)