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Q. 30

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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.