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Chapter 4: Q 188. (page 432)

Solve the system of equations.

x+y-3z=-1y-z=0-x+2y=1

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given the information

The system of equations is,

x+y-3z=-1........(1)y-z=0............(2)-x+2y=1..........(3)

02

Step 2. Finding the value of y.

Simplifying equation (2),

y-z=0y=z

03

Step 3. Eliminating y from equation (1).

Substituting y=zin the equation

x+y-3z=-1.

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

04

Step 4. Eliminating y from equation (3).

Substituting y=zin the equation

-x+2y=1.

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

05

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

Solving equations (4) and (5),

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

Adding the equations we get,

0=0

The system of equation has infinitely many solutions.

06

Step 6. Showing how x is dependent on z

Simplifying the equation x-2z=-1,

x-2z=-1x=2z-1

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