Question

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

Short answer

The solution set is $(7,6)$.

Step-by-step solution

Step 1. Given Information

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

Step 2. Solving the equation x−2y=−5 for the variable x.

$$\begin{gathered} \mathrm{Add}2y\mathrm{on}\mathrm{both}\mathrm{side} \\ x-2y+2y=-5+2y \\ x=-5+2y \end{gathered}$$

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

$$\begin{gathered} 2(-5+2y)-3y=-4 \\ -10+4y-3y=-4 \\ -10+y=-4 \\ \mathrm{Add}10\mathrm{on}\mathrm{both}\mathrm{side} \\ -10+y+10=-4+10 \\ y=6 \end{gathered}$$

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

$$\begin{gathered} x=-5+2\times 6 \\ x=-5+12 \\ x=7 \end{gathered}$$