Question

Solve the system by substitution.

$$\begin{gathered} 2x-y=1 \\ y=-3x-6 \end{gathered}$$

Short answer

The solution set is $(-1,-3)$.

Step-by-step solution

Step 1. Given Information 

We have to solve the system by substitution.

$$\begin{gathered} 2x-y=1 \\ y=-3x-6 \end{gathered}$$

Step 2. Putting the value of y in the equation 2x−y=1

$$\begin{gathered} 2x-(-3x-6)=1 \\ 2x+3x+6=1 \\ 5x+6=1 \\ \mathrm{Subtract}6\mathrm{on}\mathrm{both}\mathrm{side} \\ 5x+6-6=1-6 \\ 5x=-5 \\ \mathrm{Divide}\mathrm{by}5\mathrm{on}\mathrm{both}\mathrm{side} \\ \frac{5}{5}x=-\frac{5}{5} \\ x=-1 \end{gathered}$$

Step 3. Putting the value of x in the equation y=−3x−6

$$\begin{gathered} y=-3(-1)-6 \\ y=3-6 \\ y=-3 \end{gathered}$$