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 solution of the system of linear equations has no solutions.

Step-by-step solution

Step 1. Given Information  

The given linear equations are,

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

Step 2.  Calculation  

First solve one equation for one variable.

Solve the first equation for y.

$y=-\frac{2}{3}x+5$

Substitute $y=-\frac{2}{3}x+5$in second equation $2x+3y=11$and solve for x.

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

This is not true.

Therefore, the solution of the system of linear equations has no solutions.