SOLUTION: Find x and y in terms of a and b: ax - by = a^2 + b^2 2bx - ay = 2b^2 + 3ab - a^2 Thanks! Paul Smith

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Question 612424: Find x and y in terms of a and b:
ax - by = a^2 + b^2
2bx - ay = 2b^2 + 3ab - a^2
Thanks!
Paul Smith
Found 2 solutions by lynnlo, Edwin McCravy:
Answer by lynnlo(4176) About Me  (Show Source):
You can put this solution on YOUR website!
(1)x=by/a+a b^2/a
y=ax/b-a^2/b-b
(2)x=ay/2b+b 3a/2-a/2b
y=2bx/a-2b^2/a-3b+1

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor's answer is incorrect.

Find x and y in terms of a and b:
ax - by = a² + b²
2bx - ay = -a² + 3ab + 2b²
To eliminate y, multiply the first
equation by a and the second by -b

       a²x - aby =   a³ +  ab²
     -2b²x + aby =  a²b - 3ab² - 2b³
--------------------------------------
(a²- 2b²)x       =  a³ + a²b - 2ab² - 2b³ 
(a²- 2b²)x       = a²(a + b) - 2b²(a + b)
(a²- 2b²)x       = (a + b)(a² - 2b²)

Divide both sides by (a² - 2b²)

               x = a + b

Substitute in

         ax - by = a² + b² 

   a(a + b) - by = a² + b²

    a² + ab - by = a² + b²
      
             -by = b² - ab

Divide through by -b

               y = -b + a

               y = a - b

          (x, y) = (a+b, a-b)

Edwin