Question

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

$\left\{\begin{array}{c}3x-y=7\\ 9x-3y=21\end{array}\right.$

Short answer

The given system of equations has infinite number of solutions.

Step-by-step solution

Step 1. Given information.

The given equations are:

$\begin{array}{rcl}3x-y& =& 7\\ 9x-3y& =& 21\end{array}$

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

The first equation can be written as:

$\begin{array}{rcl}3x-y& =& 7\\ -y& =& 7-3x\\ y& =& -(7-3x)\\ y& =& 3x-7\end{array}$

Step 3. Determine the value of one variable.

Substitute the above value in the second equation.

$\begin{array}{rcl}9x-3(3x-7)& =& 21\\ 9x-9x+21& =& 21\\ 21& =& 21\end{array}$

This statement is true for all real values. So, the given system of equations has infinite number of solutions.