Question

Use elimination to solve each system of equation.

$\begin{array}{c}\mathbf{x}\mathbf{+}\mathbf{y}\mathbf{=}\mathbf{13}\\ \mathbf{x}\mathbf{-}\mathbf{y}\mathbf{=}\mathbf{5}\end{array}$

Short answer

The solution of the given system of equations is $\mathbf{(}\mathbf{9}\mathbf{,}\mathbf{4}\mathbf{)}$.

Step-by-step solution

Step 1. Write the given system of equations.

The given system of equations is:

$\begin{array}{c}x+y=13...\left(1\right)\\ x-y=5...\left(2\right)\end{array}$

Step 2. Solve the given system of equations.

Add the equations (1) and (2) to eliminate the variable $y$.

$\begin{array}{l}x+y=13\\ x-y=5\\ \overline{\text{2}x=18}\\ x=\frac{18}{2}\\ x=9\end{array}$

The value of$x$ is 9.

Substitute 9 for$x$ in the equation (1) to find the value of $y$.

$\begin{array}{c}x+y=13\\ 9+y=13\\ y=13-9\\ y=4\end{array}$

The value of$y$ is 4.

Therefore, the solution of the given system of equations is $(9,4)$.