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Chapter 4: Q 178. (page 431)

Solve the system of equations:

x+2z=04y+3z=-22x-5y=3

Short Answer

Expert verified

The solution for the system of equations is,

x=4y=1z=-2.

Step by step solution

01

Step 1. Given the information

The system of equations is,

x+2z=0.............(1)4y+3z=-2........(2)2x-5y=3...........(3)

02

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

Eliminating zwith the equations (1) and (2)

-3x-6z=0.......(1)脳-38y+6z=-4......(2)脳2

Solving the equations we get,

-3x+8y=4.....(4)

03

Step 3. Solving the equations (3) and (4) to find the value of y.

Solving the equations (3) and (4),

-6x+16y=-8........(4)脳26x-15y=9..........(3)脳3

Adding the equations we get,

16y-15y=-8+9y=1

04

Step 4. Finding the value of x.

Substituting y=1in the equation

2x-5y=3,

2x-5(1)=32x-5=32x=3+52x=8x=4

05

Step 5. Finding the value of z.

Substituting x=4in the equation

x+2z=0,

4+2z=02z=-4z=-2

06

Step 6. Checking the solution for the equation x+2z=0.

Substituting x=4y=1z=-2in the equation

x+2z=0,

4+2(-2)=04-4=00=0

This is true.

07

Step 7. Checking the solution for the equation 4y+3z=-2.

Substituting x=4y=1z=-2in the equation

4y+3z=-2,

4(1)+3(-2)=-24-6=-2-2=-2

This is true.

08

Step 8. Checking the solution for the equation 2x-5y=3.

Substituting x=4y=1z=-2in the equation

2x-5y=3

2(4)-5(1)=38-5=33=3

This is true.

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