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3 years ago

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

Mathematics

1 answer:

goblinko [34]3 years ago

5 0

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

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3 years ago

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3 years ago

Consider the differential equation <img src="https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D6%20y%5E%7

Nutka1998 [239]

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