Chapter 11: Q. 42 (page 714)

solve each system of equations. If the system has no solution, say that it is inconsistent.
$2 x + y = 4 - 2 y + 4 z = 0 3 x - 2 z = - 11$

Short Answer

Expert verified

The solution of the system of equation is

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

Step by step solution

Given information

We are given a system of equation

$2 x + y = 4 - 2 y + 4 z = 0 3 x - 2 z = - 11$

multiply equation 1 by 2 and add it to the equation 2

We get,

$4 x + 2 y = - 8$

And now

$4 x + 2 y = - 8 + - 2 y + 4 z = 0 4 x + 4 z = - 8$

Now we Multiply equation 3 by 2 and add it the new equation

We get,

$4 x + 4 z = - 8 + 6 x - 4 z = - 22 10 x = - 30$

And hence role="math" localid="1646827256666" $x = - 3$

Substitute the value of x to find the value of y,z

We get,

$2 x + y = - 4 2 (- 3) + y = - 4 - 6 + y = - 4 y = 2$

Similarly

$3 x - 2 z = - 11 3 (- 3) - 2 z = - 11 - 9 - 2 z = - 11 - 2 z = - 2 z = 1$

Conclusion

The solution of the system of equation is $x = - 3, y = 2, z = 1$

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solve each system of equations. If the system has no solution, say that it is inconsistent.
$2 x + y = 4 - 2 y + 4 z = 0 3 x - 2 z = - 11$

Short Answer

Step by step solution

Given information

multiply equation 1 by 2 and add it to the equation 2

Now we Multiply equation 3 by 2 and add it the new equation

Substitute the value of x to find the value of y,z

Conclusion

One App. One Place for Learning.

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solve each system of equations. If the system has no solution, say that it is inconsistent.2x+y=4-2y+4z=03x-2z=-11

Short Answer

Step by step solution

Given information

multiply equation 1 by 2 and add it to the equation 2

Now we Multiply equation 3 by 2 and add it the new equation

Substitute the value of x to find the value of y,z

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Statistics

Probability and Statistics

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

solve each system of equations. If the system has no solution, say that it is inconsistent.
$2 x + y = 4 - 2 y + 4 z = 0 3 x - 2 z = - 11$