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Answers without the blur. Sign up and see all textbooks for free! Q. 48

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.$2x-3y-z=0\phantom{\rule{0ex}{0ex}}3x+2y+2z=2\phantom{\rule{0ex}{0ex}}x+5y+3z=2$

The solution set for the given system is $\left\{\left(x,y,z\right)=\left(\frac{6-4z}{13},\frac{4-7z}{13},z\right)/z\in R\right\}$

See the step by step solution

## Step 1: Given information

We are given an equation

$2x-3y-z=0\left(1\right)\phantom{\rule{0ex}{0ex}}3x+2y+2z=2\left(2\right)\phantom{\rule{0ex}{0ex}}x+5y+3z=2\left(3\right)$

## Step 2: Multiply equation 1 by 2 and equation 2 by 3And then add both the equation

We get,

$2\left(2x-3y-z=0\right)\phantom{\rule{0ex}{0ex}}4x-6y-2z=0\left(4\right)\phantom{\rule{0ex}{0ex}}3\left(3x+2y+2z=2\right)\phantom{\rule{0ex}{0ex}}9x+6y+6z=5\left(5\right)$

Now we add both the equation

$4x-6y-2z=0+9x+6y+6z=413x+4z=4$

Hence we have

$13x+4z=4\phantom{\rule{0ex}{0ex}}x=\frac{4-4z}{13}$

## Step 3: Multiply equation 1 by 3 and then add it to equation 3

We get,

$3\left(2x-3y-z=0\right)\phantom{\rule{0ex}{0ex}}6x-9y-3z=0$

$3x+2y+2z=2-3x-15y-9z=-6-13y-7z=-4$

Hence we get, $-13y-7z=-4\phantom{\rule{0ex}{0ex}}y=\frac{-7z+4}{13}$

## Step 4: Conclusion

The solution set for the given equation is

$\left\{\left(x,y,z\right)=\left(\frac{6-4z}{13},\frac{4-7z}{13},z\right)/z\in R\right\}$ ### Want to see more solutions like these? 