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x−2y+3z=8, 3y+z=12, −2x+2z=−4 Enter your answer, in the form (x,y,z), in the boxes in simplest terms.

User Effect
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1 Answer

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24 votes
Answer:

(5, 3, 3)

Explanations:

The given system of equations is:

x − 2y + 3z = 8.......(1)

3y + z = 12.............(2)

−2x + 2z = −4.........(3)

Make x the subject of the formula in equation (1):

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

Substitute equation (4) into equation (3):

−2x + 2z = −4

-2(2y - 3z + 8) + 2z = -4

-4y + 6z - 16 + 2z = -4

-4y + 8z = -4 + 16

-4y + 8z = 12...............(5)

Make z the subject of the formula in equation (2):

z = 12 - 3y...........(6)

Substitute equation (6) into equation (5):

-4y + 8z = 12

-4y + 8(12 - 3y) = 12

-4y + 96 - 24y = 12

-4y - 24y = 12 - 96

-28y = -84

y = -84/-28

y = 3

Substitute y = 3 into equation (6):

z = 12 - 3y

z = 12 - 3(3)

z = 12 - 9

z = 3

Substitute y = 3 and z = 3 into equation (4)

x = 2y - 3z + 8

x = 2(3) - 3(3) + 8

x = 6 - 9 + 8

x = 5

Therefore the solution (x, y, z) to the system of equations is (5, 3, 3)

User Artyom
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