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Chapter 4: Q. 373 (page 481)

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 z from the equations (1) and (2).

Eliminating zfrom the equations (1) and (2).

2x+3y+z=12........(1)-x-y-z=-9.......(2)脳-1

Solving the equations, we get,

x+2y=3.......(4)

03

Step 3. Eliminating z from the equations (2) and (3).

Eliminating zfrom the equations (2) and (3).

-2x-2y-2z=-18..........(2)脳-23x+4y+2z=20...............(3)

Solving the equations, we get,

x+2y=2......(5)

04

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

Solving equations (4) and (5),

x+2y=3..........(4)x+2y=2..........(5)

Subtracting the equations, we get,

0=1

The system of equations has no solution.

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