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Chapter 4: Q 181. (page 432)

Solve the system of equations.

3x-z=-35y+2z=-64x+3y=-8

Short Answer

Expert verified

The solution for the system of equations is,

x=-2y=0z=-3

Step by step solution

01

Step 1. Given the information.

The system of equations is,

3x-z=-3........(1)5y+2z=-6.....(2)4x+3y=-8.....(3)

02

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

Eliminating zfrom equations (1) and (2).

6x-2z=-6........(1)脳25y+2z=-6........(2)

Solving the equations we get,

6x+5y=-12......(4)

03

Step 3. Finding the value of y.

Solving the equations (3) and (4).

12x+9y=-24.......(3)脳312x+10y=-24.....(4)脳2

Subtracting the equations we get,

-y=0y=0

04

Step 4. Finding the value of x.

Substituting y=0in the equation

4x+3y=-8.

4x+3(0)=-84x+0=-84x=-8x=-2

05

Step 5. Finding the value of z.

Substituting y=0in the equation

5y+2z=-6

5(0)+2z=-60+2z=-62z=-6z=-3

06

Step 6. Checking the solution for the equation 3x-z=-3

Substituting x=-2z=-3in the equation

3x-z=-3.

3(-2)-(-3)=-3-6+3=-3-3=-3

This is true.

07

Step 7. Checking the solution for the equation 5y+2z=-6.

Substituting y=0z=-3in the equation

5y+2z=-6

5(0)+2(-3)=-60-6=-6-6=-6

This s true.

08

Step 8. Checking the solution for the equation 4x+3y=-8.

Substituting x=-2y=0in the equation

4x+3y=-8

4(-2)+3(0)=-8-8+0=-8-8=-8

This is true.

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