Question

Solve each system by the method of addition or subtraction.

$\mathbf{9}\mathbf{x}\mathbf{-}\mathbf{2}\mathbf{y}\mathbf{=}\mathbf{50}$

$\mathbf{6}\mathbf{x}\mathbf{-}\mathbf{2}\mathbf{y}\mathbf{=}\mathbf{32}$

Short answer

The solution of given system of equations is x = 6, y = 2.

Step-by-step solution

Step 1. Description of step.

Subtract $6x-2y=32$from $9x-2y=50$and simplify.

$\begin{array}{c}\left(9x-2y\right)-\left(6x-2y\right)=50-32\\ 3x=18\end{array}$

Step 2. Description of step.

Divide each side of the equation obtained in step 1 by 3 to find the value of x.

$\begin{array}{c}\frac{3x}{3}=\frac{18}{3}\\ x=6\end{array}$

Step 3. Description of step.

Substitute 6 for xinto $6x-2y=32$and simplify.

$\begin{array}{c}6\times 6-2y=32\\ 36-2y=32\\ 2y=4\end{array}$

Step 4. Description of step.

Divide each side of the equation obtained in step 3 by 2 to find the value of y.

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

Therefore, the solution of given system of equations is x = 6, y = 2.