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Chapter 4: Q 184. (page 432)

Solve the system of equations.

2x+3y+z=12x+y+z=93x+4y+2z=20

Short Answer

Expert verified

The system of equations has no solution.

Step by step solution

01

Step 1. Given the information.

The system of equations is,

2x+3y+z=12........(1)x+y+z=9.............(2)3x+4y+2z=20.....(3)

02

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

Eliminating xfrom equations (1) and (2).

2x+3y+z=12........(1)-2x-2y-2z=-18.......(2)脳-2

Solving the equations we get,

y-z=-6........(4)

03

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

Eliminating xfrom equations (2) and (3).

-3x-3y-3z=-27........(2)脳-33x+4y+2z=20.............(3)

Solving the equations we get,

y-z=-7......(5)

04

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

Solving equations (4) and (5),

y-z=-6........(4)y-z=-7........(5)

Subtracting the equations we get,

0=1

The system of equations has no solution.

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