Question

Solve each system of equations by the substitution method.

$$\begin{gathered} y=3x+8 \\ x=y \end{gathered}$$

Short answer

The solution of the given system of equations is $x=-4$, $y=-4$.

Step-by-step solution

Step 1. Substitute the value of one variable from one equation to another.

Substitute y for x into $y=3x+8$and simplify.

$$\begin{gathered} y=3y+8 \\ 2y=-8 \end{gathered}$$

Step 2. Solve for one variable.

Divide each side of the equation obtained in step 1 to find the value of y.

$\begin{array}{c}\frac{2y}{2}=\frac{-8}{2}\\ y=-4\end{array}$

Step 3. Solve for another variable.

Substitute –4 for y into $x=y$, to find the value of x.

$x=-4$

Therefore, the solution of given system of equations is $x=-4$, $y=-4$.