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Q2.

Expert-verifiedFound in: Page 696

Book edition
7th Edition

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

Pages
948 pages

ISBN
9781337067508

**These exercises refer to the following system:**

$\left\{\begin{array}{l}x-y+z=2\\ -x+2y+z=-3\\ 3x+y-2z=2\end{array}\right.$

**To eliminate x from the third equation, we add_______ times the first equation to the third equation. The third equation becomes**

**$-3$, $4y-5z$ & $-4$**

From the given question, we have been given 3 equations

$\begin{array}{l}\text{1. x-y+z=2}\\ \text{2. -x+2 y+z=-3}\\ \text{3. 3 x+y-2 z=2}\end{array}$

An equation is a statement in that the values of two mathematical expressions are equal (indicated by the sign $=$ ).

Lets we multiple the first equation by $-3$ and add it to the third equation, the coefficients of *x *cancel each other and *x* will be eliminated:

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

Our first equation after multiplying by $-3$ is $-3\text{}x+3\text{}y-3\text{}z=-6$

Adding the above equation and equation 3 (given in the question), we get

$4\text{}y-5\text{}z=-4$

So, the third equation becomes $4\text{}y-5\text{}z=-4$.

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