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Chapter 4: Q 186. (page 432)

Solve the system of equations.

x+2y+z=4x+y-2z=3-2x-3y+z=-7

Short Answer

Expert verified

The solution for the system of equations is (5z+2,1-3z,z).

Step by step solution

01

Step 1. Given the information.

The system of equations is,

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

02

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

Eliminating xfrom equations (1) and (2),

x+2y+z=4...........(1)-x-y+2z=-3.....(2)脳-1

Solving the equations we get,

y+3z=1......(4)

03

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

Eliminating xfrom equations (2) and (3),

2x+2y-4z=6.........(2)脳2-2x-3y+z=-7.....(3)

Solving the equations we get,

-y-3z=-1.......(5)

04

Solving equations (4) and (5).

Solving equations (4) and (5), we get,

y+3x=1.......(4)-y-3x=-1...(5)

Adding the equations we get,

0=0

The system of equations has infinitely many solutions.

05

Step 5. Showing how y is dependent on z.

Simplifying the equation y+3z=1,

y+3z=1y=1-3z

06

Step 6. Showing how x is dependent on z.

Simplifying the equation x+2y+z=4

Substituting y=1-3z,

x+2(1-3z)+z=4x+2-6z+z=4x-5z=2x=2+5z.

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Determine whether the ordered pair is a solution to the system 3x+y=0x+2y=-5

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