StudySmarter AI is coming soon!

- :00Days
- :00Hours
- :00Mins
- 00Seconds

A new era for learning is coming soonSign up for free

Suggested languages for you:

Americas

Europe

Q. 44

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.

$2x+y-3z=0\phantom{\rule{0ex}{0ex}}-2x+2y+z=-7\phantom{\rule{0ex}{0ex}}3x-4y-3z=7$

The solution of the system of equation is $x=\frac{56}{13},y=-\frac{7}{13},z=\frac{35}{13}$

We are given a system of equations

$2x+y-3z=0\phantom{\rule{0ex}{0ex}}-2x+2y+z=-7\phantom{\rule{0ex}{0ex}}3x-4y-3z=7$

We get,

$-6x+6y+3z=-21$ (4)

Now add equation 1 and 4

We get,

$2x+y-3z=0-6x+6y+3z=-21-4x+7y=-21$

Hence $-4x+7y=-21$

Now we add equation 4 and 3

We get,

$3x-4y-3z=7-6x+6y+3z=-21-3x+2y=-14$

We get, $-3x+2y=-14$

We get,

$-12x+21y=-63+12x-8y=5613y=-7\phantom{\rule{0ex}{0ex}}$

Hence we get $y=-\frac{7}{13}$

We get,

$3x=2y+14\phantom{\rule{0ex}{0ex}}3x=2(-\frac{7}{13})+14\phantom{\rule{0ex}{0ex}}3x=-\frac{14}{13}+14\phantom{\rule{0ex}{0ex}}3x=\frac{168}{13}\phantom{\rule{0ex}{0ex}}x=\frac{56}{13}$

Similarly

$2x+y-3z=0\phantom{\rule{0ex}{0ex}}3z=2x+y\phantom{\rule{0ex}{0ex}}3z=2\left(\frac{56}{13}\right)-\frac{7}{13}\phantom{\rule{0ex}{0ex}}3z=\frac{105}{13}\phantom{\rule{0ex}{0ex}}z=\frac{35}{13}$

The solution of the equation are $x=\frac{56}{13},y=\frac{-7}{13},z=\frac{35}{13}$

94% of StudySmarter users get better grades.

Sign up for free