Question

Solve each system by the method of addition or subtraction.

$$\begin{gathered} 8x–y=17 \\ 6x+y=11 \end{gathered}$$

Short answer

The solution of given system of equations is $x=2$, $y=–1$.

Step-by-step solution

Step 1. Description of step.

Add $8x–y=17$and $6x+y=11$and simplify.

$(8x–y)+(6x+y)=17+11$

$14x=28$

Step 2. Description of step.

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

$\frac{14x}{14}=\frac{28}{14}$

$x=2$

Step 3. Description of step.

Substitute 2 for x into $6x+y=11$, to find the value of y.

$\begin{array}{c}6\times 2+y=11\\ 12+y=11\\ y=-1\end{array}$

Therefore, the solution of given system of equations is $x=2$, $y=–1$.