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### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

# Eliminating a VariablePerform an operation on the given system that eliminates the indicated variable. Write the new equivalent system.$\left\{\begin{array}{l}-5x+2y-3z=3\\ 10x-3y+z=-20\\ -x+3y+z=8\end{array}\right\$Eliminate the x-term from the second equation.

Hence after eliminating $x$ from the second equation, the new equivalent system is: $\left\{\begin{array}{l}-5x+2y-3z=3\\ y-5z=-14\\ -x+3y+z=8\end{array}\right\$

See the step by step solution

## Step 1. Given information

We are given the set of linear equations that is-

$\left\{\begin{array}{r}-5x+2y-3z=3\\ 10x-3y+z=-20\\ -x+3y+z=8\end{array}\right\$

## Step 2. Concept used

We have to eliminate x term from the third equation and then we have to write the new equivalent system.

## Step 3. Calculation

Since we have to eliminate x from the second equation.

Thus we are going to add the second equation with 2 times the first equation.

$\begin{array}{l}2\left(-5x+2y-3z=3\right)\\ -10x+4y-6z=6\end{array}$

We are adding the above equation with the second equation, we get

$y-5z=-14$

Now replacing the second equation with the new equation, we get the following equivalent system:

$\begin{array}{l}-5x+2y-3z=3\\ y-5z=-14\\ -x+3y+z=8\end{array}$