Question

Solve the following system in three variables using linear combinations. 3x−2y+z=0 4x+y−3z=−9 9x−2y+2z=20

Answer 1

Answer:

The solution of the system of equations is

x=2,y=7,z=8

Step-by-step explanation:

we have

3x-2y+z=0

isolate the variable z

z=2y-3x ------> equation A

4x+y-3z=-9 ----> equation B

9x-2y+2z=20 ----> equation C                  

substitute equation A in equation B and equation C

4x+y-3(2y-3x)=-9

4x+y-6y+9x=-9

13x-5y=-9 -------> equation D

9x-2y+2(2y-3x)=20

9x-2y+4y-6x=20

3x+2y=20 ----> equation E

Solve the system

13x-5y=-9 -------> equation D

3x+2y=20 ----> equation E

Multiply equation E by 2.5 both sides

2.5*(3x+2y)=20*2.5

7.5x+5y=50 -----> equation F

Adds equation D and equation F

13x-5y=-9

7.5x+5y=50

------------------

13x+7.5x=-9+50

20.5x=41

x=41/20.5

x=2

Find the value of y

substitute the value of x in the equation E

3(2)+2y=20

6+2y=20

2y=20-6

2y=14

y=7

Find the value of z

Substitute the value of x and the value of y in equation A

z=2y-3x

z=2(7)-3(2)

z=14-6

z=8

therefore

The solution of the system of equations is

x=2,y=7,z=8