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Chapter 4: Q 187. (page 432)

Solve the system of equations.

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

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

02

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

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

2x+2y-4z=6.......(1)脳2-2x-3y+z=-7....(2)

Solving the equations we get,

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

03

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

Eliminating xfrom equations (2) and (3).

-2x-3y+z=-7.......(2)2x+4y+2z=8..........(3)脳2

Solving the equations we get,

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

04

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

Solving equations (4) and (5),

y+3z=1.........(4)y+3z=1.........(5)

Subtracting the equations we get,

0=0

The solution 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+y-2z=3

Substituting y=1-3z

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

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Most popular questions from this chapter

Without graphing, determine the number of solutions and then classify the system of equations.

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