Question

Solve each system of equations by the substitution method.

$$\begin{gathered} x=8+3y \\ 2x-5y=8 \end{gathered}$$

Short answer

The solution of given system of equations is $x=-16$, $y=-8$.

Step-by-step solution

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

Substitute$8+3y$ for x into$2x-5y=8$ and simplify.

$\begin{array}{c}2\left(8+3y\right)-5y=8\\ 16+6y-5y=8\\ 16+y=8\end{array}$

Step 2. Solve for one variable.

Subtract 16 from both the sides of the equation obtained in step 1 to find the value of y.

$$\begin{gathered} 16+y-16=8-16 \\ y=-8 \end{gathered}$$

Step 3. Solve for another variable.

Substitute –8 for y into $x=8+3y$, to find the value of x.

$$\begin{gathered} x=8+3\times \left(-8\right) \\ =8-24 \\ =-16 \end{gathered}$$

Therefore, the solution of given system of equations is $x=-16$, $y=-8$.