Question

Use elimination to solve each system of equations.

$\begin{array}{c}x+3y=11\\ x+7y=19\end{array}$

Short answer

The required solution is represented by $x=5$and $y=2$.

Step-by-step solution

Step 1. Number the provided equations.

Make consideration that,

$$\begin{gathered} x+3y=11\mathrm{......}\left(1\right) \\ x+7y=19\mathrm{......}\left(2\right) \end{gathered}$$

Step 2. Perform addition between the provided equations to get the value of y after it use the obtained value to get the value of x.

Perform addition between the equation (1) and equation (2) to extract the value of y.

$$\begin{gathered} \left(x+7y\right)-\left(x+3y\right)=19-11 \\ x+7y-x-3y=8 \\ 7y-3y=8 \\ 4y=8 \\ y=\frac{8}{4} \\ y=2 \end{gathered}$$

Use the obtained value of y into equation (1) to get the value of x.

$$\begin{gathered} x+7\cdot 2=19 \\ x+14=19 \\ x=19-14 \\ x=5 \end{gathered}$$

Step 3. Write the conclusion.

The obtained value of x and y represents the required solution that is $x=5$ and $y=2$.