Q. 45 - Intermediate Algebra

Question

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

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

Step-by-Step Solution

Answer

The solution of the system of linear equations has no solutions. 

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.