• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon

### Select your language

Suggested languages for you:

Americas

Europe

Q. 44

Expert-verified
Found in: Page 714

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

### Answers without the blur.

Just sign up for free and you're in.

# 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 $x=\frac{56}{13},y=-\frac{7}{13},z=\frac{35}{13}$

See the step by step solution

## Step 1: Given information

We are given a system of equations

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

## Step 2: Multiply equation 2 by 3

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

## Step 3: Now we solve equation 4 and 5

We get,

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

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

## Step 4: Find the value x and z

We get,

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

Similarly

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

## Step 5: Conclusion

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

### Want to see more solutions like these?

Sign up for free to discover our expert answers

## Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.