Question

Solve each of the following systems of equations by the method of cross-multiplication:
5/x+y - 2/x-y =-1
15/x+y + 7/x-y = 10 where x ≠ 0, y ≠ 0

Answer 1

x = 3   & y = 2

Step-by-step explanation:

5/x+y -  2/x-y = -1

15/x+y + 7/x-y = 10

Let say u = 1/(x + y)   & v = 1/(x - y)

=> 5u  - 2v = -1       Eq 1

& 15u  + 7v = 10      Eq 2

7*Eq1 + 2 * Eq2

=> 35u + 30u = -7 + 20

=> 65u = 13

=> u = 13/65

=> u = 1/5

=> x + y = 5

Eq2 - 3 * Eq1

=> 7v - (-6v)  = 10 - (-3)

=> 13v = 13

=> v = 1

=>  x - y = 1

x + y = 5

x - y = 1

Adding both

2x = 6

=> x = 3

 & y = 2

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