Question 741683: 3x+y-6z =-10
2x+y-5z=-8
6x-3y+3z=0
Answer by only4christ(12)   (Show Source):
You can put this solution on YOUR website! First, I will get a system of equations in two variables. I will number the equations so you can keep up with what's going on.
#1 3x+y-6z =-10
#2 2x+y-5z=-8
#3 6x-3y+3z=0
First, multiply #1 by 3
3(3x+y-6z=-10) this gives you 9x+3y-18z=-30 (this is #4)
Add #3 + #4, you get 15x - 15z = -30 (this is #6)
Next, multiply #2 by 3
3(2x+y-5z=-8) this gives you 6x-3y-15z=-24 ( this is #5)
Add: #3 + #5, you get 12x - 12z = -24 (this is #7)
Now, we will work with the systems of equations we found in two variables in equations #6 & #7
#6 15x-15z=-30
#7 12x-12z=-24
To eliminate, let's say x, I'll multiply #6 by -4 and #7 by 5
-4(15x-15z=-30) = -60x+60z=-120 (this is #8)
5(12x-12z=-24) = 60x-60z=120 (this is #9)
Add: #8 + #9, you get 0 = 0.....all the variables cancel out.
This means your answer is Infinitely Many Solutions. Meaning any solution set you choose for x, y, z will work.
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