Question

In the following exercises, solve the systems of equations by substitution.
$$\begin{gathered} 2x+y=-2 \\ 3x-y=7 \end{gathered}$$

Short answer

The solution set is $(1,-4)$.

Step-by-step solution

Step 1. Given Information

In the following exercises, we have to solve the systems of equations by substitution.
$$\begin{gathered} 2x+y=-2 \\ 3x-y=7 \end{gathered}$$

Step 2. Solving the equation 2x+y=−2 for the variable y.

$$\begin{gathered} \mathrm{Subtract}2x\mathrm{on}\mathrm{both}\mathrm{side} \\ 2x+y-2x=-2-2x \\ y=-2-2x \end{gathered}$$

Step 3. Putting the value of y in the equation 3x−y=7.

$$\begin{gathered} 3x-(-2-2x)=7 \\ 3x+2+2x=7 \\ 5x+2=7 \\ Subtract2onbothside \\ 5x+2-2=7-2 \\ 5x=5 \\ Divideby5onbothside \\ \frac{5}{5}x=\frac{5}{5} \\ x=1 \end{gathered}$$

Step 4. Putting the value of x in the equation y=−2-2x.

$$\begin{gathered} y=-2-2\times 1 \\ y=-2-2 \\ y=-4 \end{gathered}$$