vinay1983 wrote:3/(x+y) + 2/(x-y) = 3/2
9/(x+y) - 4/(x-y)= -1/2
Solve the equations.
To clear the coefficients in red, multiply the first equation by 2:
6/(x+y) +
4/(x-y) = 6/2.
Add the equations and simplify:
6/(x+y) +
4/(x-y) = 6/2.
9/(x+y) -
4/(x-y) = -1/2
_________________________
15/(x+y) = 5/2
30 = 5(x+y)
x+y = 6.
To clear the coefficients in blue, multiply the first equation by -3:
-9/(x+y) - 6/(x-y) = -9/2.
Add the equations and simplify:
-9/(x+y) - 6/(x-y) = -9/2.
9/(x+y) - 4/(x-y) = -1/2
_________________________
-10/(x-y) =-10/2
-20 = -10(x-y)
x-y = 2.
Add together the resulting equations:
x+y = 6
x-y = 2
________
2x = 8
x = 4.
Substitute x=4 into x+y=6:
4+y=6
y = 2.
Thus, x=4 and y=2.
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