solve the following simultaneous equation

Question

x+y+1/ x-y-1 =2

x+y-1 / x-y-1= -1

Answer 1

(x + y + 1) / (x - y - 1) = 2

(x + y - 1) / (x - y - 1) = -1

multiply both sides by x - y - 1

x + y + 1 = 2(x - y - 1)

x + y - 1 = -1(x - y - 1)

expand and simplify

x + y + 1 = 2x - 2y - 2

x + y - 1 = -x + y + 1

.

-x + 3y = -3

2x + 0y = 2

second equation: 2x = 2, so x = 1

first equation:  -1 + 3y = -3

3y = -2

y = -2/3

.

Important!  Since we have a fraction, we need to check if our answer makes the bottom zero.

x - y - 1

1 - (-2/3) - 1

1 + 2/3 - 1

2/3

The answer does not make the bottom of the fraction zero, so we're allowed to use that answer.

Answer:  x = 1, y = -2/3