SOLUTION: 7. Solve {{{system(x+3y-z = -2, 4x+6y+3z = 4, 2x-y+2z = 10)}}}

Algebra ->  Graphs -> SOLUTION: 7. Solve {{{system(x+3y-z = -2, 4x+6y+3z = 4, 2x-y+2z = 10)}}}      Log On


   

Question 143738: 7. Solve system%28x%2B3y-z+=+-2%2C+4x%2B6y%2B3z+=+4%2C+2x-y%2B2z+=+10%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%2B3y-z=-2 Equation 1
4x%2B6y%2B3z=4 Equation 2
2x-y%2B2z=10 Equation 3



2%28x%2B3y-z%29=2%28-2%29 Multiply both sides of Equation 1 by 2


2x%2B6y-2z=-4 Distribute and multiply. Let's call this Equation 4


Now add Equation 4 to Equation 3 and call the result Equation 5

2x%2B6y-2z=-4 Equation 4
+2x-y%2B2z=10 Equation 3
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4x%2B5y=6 Equation 5





3%28x%2B3y-z%29=3%28-2%29 Multiply both sides of Equation 1 by 3


3x%2B9y-3z=-6 Distribute and multiply. Let's call this Equation 6


Now add Equation 5 to Equation 2 and call the result Equation 7

3x%2B9y-3z=-6 Equation 5
+4x%2B6y%2B3z=4 Equation 2
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7x%2B15y=-2 Equation 7



So we now have the two equations Equation 5 and Equation 7


4x%2B5y=6 Equation 5
7x%2B15y=-2 Equation 7


-3%284x%2B5y%29=-3%286%29 Multiply both sides of Equation 5 by -3
7x%2B15y=-2 Equation 7



-12x-15y=-18 Distribute
7x%2B15y=-2 Equation 7



Now add the equations

-12x-15y=-18
+7x%2B15y=-2
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-5x=-20


x=%28-20%29%2F%28-5%29 Divide both sides of the resulting equation by -5 to isolate x


x=4 Reduce. So this is the first part of our answer.


7x%2B15y=-2 Go back to Equation 7


7%284%29%2B15y=-2 Plug in x=4


28%2B15y=-2 Multiply


15y=-2-28Subtract 28 from both sides


15y=-30 Combine like terms on the right side


y=%28-30%29%2F%2815%29 Divide both sides by 15 to isolate y



y=-2 Reduce. So this is the second part of our answer.



x%2B3y-z=-2 Go back to Equation 1


4%2B3%28-2%29-z=-2 Plug in x=4 and y=-2


4-6-z=-2 Multiply



-z-2=-2 Combine like terms on the left side


-z=-2%2B2Add 2 to both sides


-z=0 Combine like terms on the right side


z=%280%29%2F%28-1%29 Divide both sides by -1 to isolate z



z=0 Divide. So this is the third part of our answer.


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Answer:

So our answer is

x=4,y=-2 and z=0


which forms the point (4,-2,0)