Question

Use substitution to solve each system of equation.

$\begin{array}{c}\mathbf{y}\mathbf{=}\mathbf{x}\mathbf{+}\mathbf{8}\\ \mathbf{2}\mathbf{x}\mathbf{+}\mathbf{y}\mathbf{=}\mathbf{-}\mathbf{10}\end{array}$

Short answer

The solution of the given system of equations is$\mathbf{(}\mathbf{-}\mathbf{6}\mathbf{,}\mathbf{2}\mathbf{)}$.

Step-by-step solution

Step 1. Write the given system of equations.

The given system of equations is:

$\begin{array}{l}y=x+8\text{...}\left(1\right)\\ 2x+y=-10\text{...}\left(2\right)\end{array}$

Step 2. Solve the given system of equations.

Substitute the value of $y$ from the equation (1) in the equation (2).

$\begin{array}{c}2x+y=-10\\ 2x+x+8=-10\\ 3x+8=-10\\ 3x=-10-8\\ 3x=-18\\ x=\frac{-18}{3}\\ x=-6\end{array}$

The value of $x$is $-6$.

Substitute$-6$ for$x$ in the equation (1) to find the value of $y$.

$\begin{array}{c}y=x+8\\ =-6+8\\ =2\end{array}$

The value of $y$is 2.

Therefore, the solution of the given system of equations is $(-6,2)$.