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Chapter 4: Q. 372 (page 481)

Solve the system of equations.

5x+3y=-62y+3z=-17x+z=1

Short Answer

Expert verified

The solution for the system of equations is,

x=0y=-2z=1.

Step by step solution

01

Step 1. Given the information.

The system of equations is,

5x+3y=-6...........(1)2y+3z=-1...........(2)7x+z=1................(3)

02

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

Eliminating zfrom equations (2) and (3).

2y+3z=-1.........(2)-21x-3z=-3....(3)脳-3

Solving the equations, we get,

-21x+2y=-4.........(4)

03

Step 3. Finding the value of x.

Solving equation (1) and (4)

10x+6y=-12........(1)脳2-63x+6y=-12.....(2)脳3

Subtracting the equations, we get,

73x=0x=0

04

Step 4. Finding the value of y.

Substituting x=0in the equation

5x+3y=-6,

5(0)+3y=-60+3y=-63y=-6y=-2

05

Step 5. Finding the value of z.

Substituting x=0in the equation

7x+z=1,

7(0)+z=10+z=1z=1

06

Step 6. Checking the solution for the equation 5x+3y=-6.

Substituting x=0y=-2in the equation

5x+3y=-6,

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

This is true.

07

Step 7. Checking the solution for the equation 2y+3z=-1

Substituting y=-2z=1in the equation

2y+3z=-1,

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

This is true.

08

Step 8. Checking the solution for the equation 7x+z=1.

Substituting x=0z=1in the equation

7x+z=1,

7(0)+1=10+1=11=1

This is true.

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