Question

In the following exercises, solve the systems of equations by substitution.
$$\begin{gathered} 2x+y=-4 \\ 3x-2y=-6 \end{gathered}$$

Short answer

The solution set is $(-2,0)$.

Step-by-step solution

Step 1. Given Information

In the following exercises, we have to solve the systems of equations by substitution.
$$\begin{gathered} 2x+y=-4 \\ 3x-2y=-6 \end{gathered}$$

Step 2. Solving the equation 2x+y=−4 for the variable y.

$$\begin{gathered} \mathrm{Subtract}2x\mathrm{on}\mathrm{both}\mathrm{side} \\ 2x+y-2x=-4-2x \\ y=-4-2x \end{gathered}$$

Step 3. Putting the value of y in the equation 3x−2y=−6.

$$\begin{gathered} 3x-2(-4-2x)=-6 \\ 3x+8+4x=-6 \\ 7x+8=-6 \\ \mathrm{Subtract}8\mathrm{on}\mathrm{both}\mathrm{side} \\ 7x+8-8=-6-8 \\ 7x=-14 \\ \mathrm{Divide}\mathrm{by}7\mathrm{on}\mathrm{both}\mathrm{side} \\ \frac{7}{7}x=-\frac{14}{7} \\ x=-2 \end{gathered}$$

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

$$\begin{gathered} y=-4-2(-2) \\ y=-4+4 \\ y=0 \end{gathered}$$