Question

Solve the system of equation$\left\{\begin{array}{l}y=-x-1\\ y=x+7\end{array}\right.$by substitution

Short answer

The solution is$\left(-4,3\right)$

Step-by-step solution

Step 1. Given information 

The given equations are:

$y=-x-1\cdots \cdots \left(1\right)$

$y=x+7\cdots \cdots \left(2\right)$

Step 2. Substitute value of y from equation 1 in equation 2

$\Rightarrow -x-1=x+7$

Step 3. Solve for x

$\Rightarrow -x-x=7+1$

$\Rightarrow -2x=8$

$\Rightarrow x=-\frac{8}{2}$

$\Rightarrow x=-4$

Step 4. Substitute value of x from step 3 in equation 1

$\Rightarrow y=-\left(-4\right)-1$

$\Rightarrow y=4-1$

$\Rightarrow y=3$

Step 5. Checking solution  

Now we have $x=-4$and $y=3$

Put these values in equation $\left(1\right)$

role="math" localid="1649177141599" $\Rightarrow 3=-\left(-4\right)-1$

$\Rightarrow 3=3$

Also put these values in equation $\left(2\right)$

$\Rightarrow 3=-4+7$

$\Rightarrow 3=3$