Question

solve for x and y

10/x+y +2/x-y =4
15/x+y - 5/x-y= -2

(x+y is not equal to 0 and x-y is not equal to 0)

Answer 1

let x+y=p
let x-y=q
10p+2q=4 equation (1)
15p-5q=-2 equation (2)

equation(1) multiply by 5
equation (2) multiply by 2

50p+10q=20
30p+-10q=-10
80p=10
p=1/8

subtitute the value of p in equation (1)
10(1/8)+2q=4
2q=4 -5/4
q=16-5/4
q=11/4

x+y=p
x+y=1/8
8x+8y=1 (3)

x-y=q
x-y=11/
4x-4y=11 (4)

8x+8y=1
4x-4y=11

equation (3) multiply by 2
8x+8y=1
8x-8y=22
16x=23
x=23/16

subtitute x in (4)
4x-4y=11
4(23/16) -4y=11
23/4 -4y=11
-4y=11 -23/4
-4y=44/4-23/4
-4y=21
y=-21/4

there fore x=23/16 y =-21/4
i hope you will understand