Question

In the following exercises, solve the systems of equations by substitution.

$$\begin{gathered} y=-\frac{2}{3}x+5 \\ 2x+3y=11 \end{gathered}$$

Short answer

The system of equations has no solution.

Step-by-step solution

Step 1. Given Information  

The given equations are

$$\begin{gathered} y=-\frac{2}{3}x+5 \\ 2x+3y=11 \end{gathered}$$

Step 2. Calculation 

Substitute the equation first in the second equation to find the value of variable x.

$$\begin{gathered} 2x+3y=11 \\ 2x+3(-\frac{2}{3}x+5)=11 \\ 2x-2x+15=11 \\ 0\ne -4 \end{gathered}$$

Since $0\ne -4$is a false statement, the system of equations is inconsistent. The graph of these two equations would be the parallel line. Thus the system of the linear equation has no solution.