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Chapter 4: Q 183. (page 432)

Solve the system of equations,

x-2y+2z=1-2x+y-z=2x-y+z=5

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,

x-2y+2z=1......(1)-2x+y-z=2.....(2)x-y+z=5.........(3)

02

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

Eliminating xfrom equations (1) and (2),

2x-4y+4z=2..........(1)脳2-2x+y-z=2...........(2)

Solving the equations we get,

role="math" localid="1644567307021" -3y+3z=4........(4)

03

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

Eliminating xfrom equations (2) and (3).

-2x+y-z=2........(2)2x-2y+2z=10.....(3)脳2

Solving the equations we get,

-y+z=12.......(5)

04

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

Solving equations (4) and (5),

-3y+3z=4.......(4)-3y+3z=36......(5)脳3

Subtracting the equations we get,

0=-32

The system of equations has no solution.

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