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Q14.

Expert-verifiedFound in: Page 697

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

**Eliminating a Variable**

**Perform 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: $\left\{\begin{array}{l}-5x+2y-3z=3\\ y-5z=-14\\ -x+3y+z=8\end{array}\right.$

We are given the set of linear equations that is-

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

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

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.

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

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:

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

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