Question

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$\left\{\begin{array}{c}x-y=5\\ -3x+3y=2\end{array}\right.$

Short answer

The given system of equations is inconsistent.

Step-by-step solution

Step 1. Given information.

The given equations are:

$\begin{array}{rcl}x-y& =& 5\\ -3x+3y& =& 2\end{array}$

Step 2. Determine one variable in terms of another variable.

The first equation can be written as:

$\begin{array}{rcl}x-y& =& 5\\ x& =& 5+y\end{array}$

Step 3. Determine the value of one variable.

Substitute the above value in the second equation.

$\begin{array}{rcl}-3(5+y)+3y& =& 2\\ -15-3y+3y& =& 2\\ -15& =& 2\end{array}$

This statement is false, it means the system has no solution. So, the given system of equations is inconsistent.