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Q. 48

Expert-verifiedFound in: Page 714

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 $\left\{\right(x,y,z)=(\frac{6-4z}{13},\frac{4-7z}{13},z)/z\in R\}$

We are given an equation

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

We get,

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

Now we add both the equation

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

Hence we have

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

We get,

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

And now we add,

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

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

The solution set for the given equation is

$\left\{\right(x,y,z)=(\frac{6-4z}{13},\frac{4-7z}{13},z)/z\in R\}$

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