Question

Solve a System of Equations by Elimination -

$$\begin{gathered} 5x-3y=15 \\ y=\frac{5}{3}x-2 \end{gathered}$$

Short answer

This statement is false. The equations are inconsistent and so their graphs would be parallel lines. The system does not have a solution.

Step-by-step solution

Step 1.  Given Data

Equation - $$\begin{gathered} 5x-3y=15 \\ y=\frac{5}{3}x-2 \end{gathered}$$

Step 2.  To Find

Solve a System of Equations by Elimination and find the value of x and y.

Step 3.  Explanation

Equation -

$$\begin{gathered} 5x-3y=15 \\ y=\frac{5}{3}x-2 \end{gathered}$$

Write the second equation in standard form -

$$\begin{gathered} 5x-3y=15 \\ \frac{5}{3}x-y=2 \end{gathered}$$

Clear the fractions by multiplying the second equation by 3 -

$$\begin{gathered} 5x-3y=15 \\ (\frac{5}{3}x-y)\times 3=2\times 3 \\ 5x-3y=15 \\ 5x-3y=6 \end{gathered}$$

Step 4.  Calculation

The equation become -

$$\begin{gathered} 5x-3y=15 \\ 5x-3y=6 \end{gathered}$$

We Subtract the x's and y's and constants -

$\begin{array}{l}5x-3y=15\\ \frac{5x-3y=6}{0\ne 9}\end{array}$

This statement is false. The equations are inconsistent and so their graphs would be parallel lines. The system does not have a solution.