Question

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

$\left\{\begin{array}{l}-x+3y=8\\ 2x-6y=-20\end{array}\right.$

Short answer

The system of equations$\left\{\begin{array}{l}-x+3y=8\\ 2x-6y=-20\end{array}\right.$has no solution.

Step-by-step solution

Step 1. Given Information

We are given a system of equations $\left\{\begin{array}{l}-x+3y=8\\ 2x-6y=-20\end{array}\right.$

The objective is to solve the equation using the elimination method.

Step 2. Using the elimination method

Multiply the first equation by $2$and add it with the second equation

$\begin{array}{rcl}2(-x+3y)+2x-6y& =& 2\times 8+(-20)\\ -2x+6y+2x-6y& =& 16-20\\ 0& =& -4\end{array}$

This gives us a false statement. So the given system of equations has no solution.