Question

e solution of the system of equations.

$8x + y = -13$

$-8x - 2y = 10$

Explanation:

Step1: Add the two equations

Add the equations \(8x + y = -13\) and \(-8x - 2y = 10\) together.
\[

$$\begin{align*} (8x + y) + (-8x - 2y) &= -13 + 10\\ 8x + y - 8x - 2y &= -3\\ -y &= -3 \end{align*}$$

\]

Step2: Solve for y

Multiply both sides of \(-y = -3\) by \(-1\) to get \(y\).
\[y = 3\]

Step3: Substitute y into first equation

Substitute \(y = 3\) into \(8x + y = -13\).
\[

$$\begin{align*} 8x + 3 &= -13\\ 8x &= -13 - 3\\ 8x &= -16 \end{align*}$$

\]

Step4: Solve for x

Divide both sides of \(8x = -16\) by \(8\).
\[x = \frac{-16}{8} = -2\]

Answer:

The solution is \(x = -2\), \(y = 3\)