SOLUTION: Solve for x and y 15/x-y + 22/x+y = 5 40/x-y + 55/x+y =13

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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): You can put this solution on YOUR website!
Solve for x and y
+ = 5
+ = 13
use elimination, multiply the 1st equation by 8, the 2nd equation by 3
+ = 40
+ = 39
------------------subtraction eliminates (x-y), find (x+y)
= 1
x + y = 11
:
use elimination again, multiply the 1st equation by 5, the 2nd equation by 2
subtract the 1st equation from the 2nd eq
+ = 26
+ = 25
--------------------subtraction eliminates (x+y), find (x-y)
= 1
x - y = 5
:
Use elimination a 3rd time with these two equation
x + y = 11
x - y = 5
---------------Adding eliminates y, find x
2x = 16
x = 16/2
x = 8
:
I will let do the easy job of finding y. Check the solutions in the original problem
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
~~~~~~~~~~~~~~~~~~~~~~~ 

 = ,    (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): 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
Easiest method: Elimination. This should produce:  

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