Question

solve 5/x+y -2/x-y= -1 and 15/x+y +7/x-y

Answer 1

let 1/x+y=a, 1/x-y=b
Then,
5a-2b=-1 ----------(1)
15a+7b=10 ------------(2)
multiply by 3 into equation and subtracting equation (2) from (1)
15a-6b=-3
15a+7b=10
- - -
__________
-13b =-13
$b = - 13 \div - 13$
b=1
1/x-y=1 ------------(3)
x-y=1
put the value of b into equation (2)
15a+7×1=10
15a+7 =10
15a=10-7
a=3/15
a=1/15
1/x+y = 1/15
x+y=15 ------------(4)
adding equation (3) &(4)
x+y=15
x-y=1
_______
2x =16
x=16/2
x=8
puting the value of x into equation (4)
8-y=1
-y=1-8
-y=-7
y =7


hence ,
x=8,y=7