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Chapter 4: Q 185. (page 432)

Solve the system of equations.

x+4y+z=-84x-y+3z=92x+7y+z=0

Short Answer

Expert verified

The system of equations has no real solution.

Step by step solution

01

Step 1. Given the information.

The system of equations is,

x+4y+z=-8.........(1)4x-y+3z=9..........(2)2x+7y+z=0.........(3)

02

Step 2. Eliminating x from equations (1) and (2).

Eliminating xfrom equations (1) and (2),

-4x-16y-4z=32........(1)脳-44x-y+3z=9...............(2)

Solving the equations we get,

-17y-z=41......(4)

03

Step 3. Eliminating x from equations (2) and (3).

Eliminating xfrom equations (2) and (3),

4x-y+3z=9...............(2)-4x-14y-2z=0........(3)脳-2

Solving the equations we get,

-15y+z=9........(5)

04

Step 4. Solving equations (4) and (5).

Solving equations (4) and (5),

-17y-z=41........(4)-15y+z=9.........(5)

Solving the equations we get,

-32y=50y=-5032y=-2516

Here we cannot get any real solution.

The system of equations has no real solution.

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