SOLUTION: solve for y in the equation 3/x - 4/y + 6/z = 1 9/x + 8/y - 12/z = 3 9/x - 4/y + 12/z = 4

Algebra ->  Expressions-with-variables -> SOLUTION: solve for y in the equation 3/x - 4/y + 6/z = 1 9/x + 8/y - 12/z = 3 9/x - 4/y + 12/z = 4      Log On


   

Question 883491: solve for y in the equation
3/x - 4/y + 6/z = 1
9/x + 8/y - 12/z = 3
9/x - 4/y + 12/z = 4
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
It is easy to solve the system if we make
a=1%2Fx, b=1%2Fy , and c=1%2Fz
After that, we just write
system%283a-4b%2B6c=1%2C9a%2B8b-a2c=3%2C9a-4b%2B12c=4%29 and solve for b .
Multiplying the first equation times 2 and adding the second equation we get
6a-8b%2B12c=2
9a%2B8b-12c=3
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15a=5 ----> a=5%2F15 ---> a=1%2F3
Adding the second and third equations we get
6a-8b%2B12c=2
9a-4b%2B12c=4
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18a%2B4b=7
With the two resulting equations without a c , we solve for b
system%28a=1%2F3%2C18a%2B4b=7%29 ---> 18%2A%281%2F3%29%2B4b=7-->6%2B4b=7-->4b=7-6-->4b=1-->b=1%2F4
So, system%28b=1%2Fy%2Cb=1%2F4%29 ---> highlight%28b=4%29 ---> highlight%28y=1%2F4%29