Chapter 11: Q. 41 (page 714)

solve each system of equations. If the system has no solution, say that it is inconsistent.
$x - y = 6 2 x - 3 z = 16 2 y + z = 4$

Short Answer

Expert verified

The solution of the equation is $x = 8 y = 2 z = 0$

Step by step solution

Given information

We are given

$x - y = 6 2 x - 3 z = 16 2 y + z = 4$

Now multiply equation 1 by 2 and subtract from equation 3

We get,

$2 x - 2 y = 12$

Now we add this in equation 3 we get,

$2 x - 2 y = 12 + 2 y + z = 4 2 x + z = 16$

Now we subtract equation from 2,

We get,

$2 x + z = 16 - 2 x + 3 z = 16 4 z = 0$

Hence $z = 0$

Now substitute the value of z to find the value of x and y

We get,

$2 x - 3 z = 16 2 x = 16 x = 8$

Now we find the values of y

$2 y + z = 4 2 y = 4 y = 2$

Conclusion

The solution of system of equation is

$x = 8 y = 2 z = 0$

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solve each system of equations. If the system has no solution, say that it is inconsistent.
$x - y = 6 2 x - 3 z = 16 2 y + z = 4$

Short Answer

Step by step solution

Given information

Now multiply equation 1 by 2 and subtract from equation 3

Now we subtract equation from 2,

Now substitute the value of z to find the value of x and y

Conclusion

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solve each system of equations. If the system has no solution, say that it is inconsistent.x-y=62x-3z=162y+z=4

Short Answer

Step by step solution

Given information

Now multiply equation 1 by 2 and subtract from equation 3

Now we subtract equation from 2,

Now substitute the value of z to find the value of x and y

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Decision Maths

Mechanics Maths

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

solve each system of equations. If the system has no solution, say that it is inconsistent.
$x - y = 6 2 x - 3 z = 16 2 y + z = 4$