Question

In the following exercises, solve the systems of equations by substitution.
$$\begin{gathered} x-3y=-9 \\ 2x+5y=4 \end{gathered}$$

Short answer

The solution set is $(-3,2)$.

Step-by-step solution

Step 1. Given Information

In the following exercises, we have to solve the systems of equations by substitution.
$$\begin{gathered} x-3y=-9 \\ 2x+5y=4 \end{gathered}$$

Step 2. Solving the equation x−3y=−9 for the variable x.

$$\begin{gathered} \mathrm{Add}3y\mathrm{on}\mathrm{both}\mathrm{side} \\ x-3y+3y=-9+3y \\ x=-9+3y \end{gathered}$$

Step 3. Putting the value of x in the equation 2x+5y=4.

$$\begin{gathered} 2(-9+3y)+5y=4 \\ -18+6y+5y=4 \\ -18+11y=4 \\ \mathrm{Add}18\mathrm{on}\mathrm{both}\mathrm{side} \\ -18+11y+18=4+18 \\ 11y=22 \\ \mathrm{Divide}\mathrm{by}11\mathrm{on}\mathrm{both}\mathrm{side} \\ \frac{11}{11}y=\frac{22}{11} \\ y=2 \end{gathered}$$

Step 4. Putting the value of y in the equation x=−9+3y.

$$\begin{gathered} x=-9+3\times 2 \\ x=-9+6 \\ x=-3 \end{gathered}$$