If x and y in the equations (2)/( x - 1) - (1)/(y + 2) = 10 \\ (3)/(y + 2) + (1)/(x - 1) = - 9 what's the value of x + y = … a. -2 b. -1 c. -11/12 d. -5/6 e. -3/4

Question

If x and y in the equations


`(2)/( x - 1) - (1)/(y + 2) = 10 \\ (3)/(y + 2) + (1)/(x - 1) = - 9`
what's the value of x + y = …

a. -2
b. -1
c. -11/12
d. -5/6
e. -3/4

Answer 1

We can let
a = 1/(x-1)
b = 1/(y+2)
and rewrite the equations as
2a - b = 10
a + 3b = -9
Using the first to write an expression for b, we get
b = 2a - 10
Substituting this into the second equation gives
a + 3(2a -10) = -9
7a -30 = -9 . . . . . . . . simplify
7a = 21 . . . . . . . . . . .add 30
a = 3
b = 2·3 - 10 = -4

Now, we can find x and y.
3 = 1/(x -1)
x - 1 = 1/3
x = 1 1/3 = 4/3

-4 = 1/(y +2)
y +2 = -1/4
y = -2 1/4 = -9/4

Then the desired sum is
x + y = 4/3 -9/4 = (16 -27)/12
x + y = -11/12

The appropriate choice is ..
c. -11/12