Question

Use elimination to solve each system of equations.

$\begin{array}{c}\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{6}\mathbf{y}\mathbf{=}\mathbf{18}\\ \mathbf{3}\mathbf{x}\mathbf{+}\mathbf{2}\mathbf{y}\mathbf{=}\mathbf{13}\end{array}$

Short answer

The solution of the given system of equations is $\mathbf{(}\mathbf{3}\mathbf{,}\mathbf{2}\mathbf{)}$.

Step-by-step solution

Step 1. Write the given system of equations.

The given system of equations is:

$\begin{array}{c}2x+6y=18......\left(1\right)\\ 3x+2y=13......\left(2\right)\end{array}$

Step 2. Solve the given system of equations.

Multiply the both sides of the equation (2) by 3.

$\begin{array}{l}(3x+2y)\times 3=13\times 3\\ 9x+6y=39\left(3\right)\end{array}$

Subtract the equation (3) from equation (1) to eliminate the variable $y$.

$\begin{array}{l}\text{2x}+6y=18\\ \text{9}x+6y=39\\ \underset{¯}{---}\\ -7x=-21\\ x=\frac{-21}{-7}\\ x=3\end{array}$

The value of$x$ is 3.

Substitute 3 for$x$ in the equation (1) to find the value of $y$.

$\begin{array}{c}2x+6y=18\\ 2\left(3\right)+6y=18\\ 6+6y=18\\ 6y=18-6\\ 6y=12\\ y=\frac{12}{6}\\ y=2\end{array}$

The value of$y$ is 2.

Therefore, the solution of the given system of equations is $(3,2)$.