SOLUTION: 3x+6y-z=6 3x-3y+5z=-6 9x+9y-2z=11

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Question 1203438: 3x+6y-z=6
3x-3y+5z=-6
9x+9y-2z=11
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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9x+18y-3z=18
9x-9y+15z=-18
9x+9y-2z=11
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Peform E1-E3 and E2-E3.

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9y-z=7
-18y+17z=-29
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Make 2*E1.
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18y-2z=14
-18y+17z=-29
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Perform E1+E2.

15z=-15

z=-1
With this, you can go back and find values for y and x.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There are an endless number of different ways to solve this system of equations; the other tutor has shown one.

Like the other tutor, I changed the three equations into equivalent forms to get "9x" as a term in all three equations. Then from there I went a different direction the they did.

9x%2B18y-3z=18 [1]
9x-9y%2B15z=-18 [2]
9x%2B9y-2z=11 [3]

Do [1]-[2] to eliminate x to get one equation in y and z; do [1]-[3] to get another.

27y-18z=36 --> 9y-6z=12 [4]
9y-z=7 [5]

Do [4]-[5] to eliminate y and solve for z

-5z=5
z=-1

Substitute z=-1 in [5] and solve for y

9y%2B1=7
9y=6
y=6%2F9=2%2F3

Substitute z=-1 and y=2/3 in [1] to solve for x

9x%2B12%2B3=18
9x%2B15=18
9x=3
x=3%2F9=1%2F3

ANSWER: (x,y,z) = (1/3,2/3,-1)