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Question 1036350: Solve for x and y
15/x-y + 22/x+y = 5
40/x-y + 55/x+y =13
Found 3 solutions by ankor@dixie-net.com, ikleyn, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source):
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! Solve for x and y
15/x-y + 22/x+y = 5
40/x-y + 55/x+y =13
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 =  , (1)
 =  . (2)
The standard way to solve problems like this, is to introduce new variables
u =  , (3)
v =  . (4)
Then the system of non-linear equations (1) and (2) becomes the system of linear equations
15u + 22v = 5, (5)
40u + 55v = 13. (6)
To solve it, apply the Elimination method. Multiply equation (5) by 8 (both sides) and multiply the equation (6) by 3,
then distract. You will get
176v - 165v = 40 - 39 ---> 11v = 1 ---> v =  .
Now, from (5)
15u = 5 - 22v =  ---> 15u = 3 ---> u =  =  .
Returning back to the original unknowns x and y, you have
x - y = 5, (7)
x + y = 11. (8)
Now we are at the finish line. Add (7) and (8), and you will get
2x = 16 ---> x =  = 8.
From (8), y = 11 - x = 11 - 8 = 3.
Answer. x = 8, y = 3.
The lesson to learn is the method of introducing these new variables.
Answer by MathTherapy(10552)  (Show Source):
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