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Expert-verified Found in: Page 714 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # 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\$

The given system of equations has infinite number of solutions.

See the 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:

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

## Step 3. Determine the value of one variable.

Substitute the above value in the second equation.

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

This statement is true for all real values. So, the given system of equations has infinite number of solutions. ### Want to see more solutions like these? 