Chapter 11: Q. 43 (page 714)

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$x - 2 y + 3 z = 7 2 x + y + z = 4 - 3 x + 2 y - 2 z = - 10$

Short Answer

Expert verified

The solution of the system of equation is $x = 2, y = - 1, z = 1$

Step by step solution

Given information

We are given a system of equation

$x - 2 y + 3 z = 7 2 x + y + z = 4 - 3 x + 2 y - 2 z = - 10$

Multiply equation 2 by 2

We get,

$4 x + 2 y + 2 z = 8$ (4)

Now add this to equation 2

We get,

$x - 2 y + 3 z = 7 + 4 x + 2 y + 2 z = 8 5 x + 5 z = 15$

Hence

$5 x + 5 z = 15 x + z = 3$ (5)

Now subtract equation (4) from equation 3

$- 3 x + 2 y - 2 z = - 10 - 4 x - 2 y - 2 z = - 8 - 7 x - 4 z = - 18$

$- 7 x - 4 z = - 18$ (6)

Find the value of x

Multiply equation 5 by 4 And add it to equation 6

We get,

$4 x + 4 z = 12$

Now we add this to equation 6

We get,

$4 x + 4 z = 12 - 7 x - 4 z = - 18 - 3 x = - 6$

hence $x = 2$

Find the value of y and z

We get,

$x + z = 3 2 + z = 3 z = 1$

And

$x - 2 y + 3 z = 7 2 - 2 y + 3 = 7 - 2 y = 2 y = - 1$

Conclusion

The solution of the system of equation is $x = 2, y = - 1, z = 1$

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Solve each system of equations. If the system has no solution, say that it is inconsistent.
$x - 2 y + 3 z = 7 2 x + y + z = 4 - 3 x + 2 y - 2 z = - 10$

Short Answer

Step by step solution

Given information

Multiply equation 2 by 2

Find the value of x

Find the value of y and z

Conclusion

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Solve each system of equations. If the system has no solution, say that it is inconsistent. x-2y+3z=72x+y+z=4-3x+2y-2z=-10

Short Answer

Step by step solution

Given information

Multiply equation 2 by 2

Find the value of x

Find the value of y and z

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Logic and Functions

Statistics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$x - 2 y + 3 z = 7 2 x + y + z = 4 - 3 x + 2 y - 2 z = - 10$