Question

Find x and y if $\frac{1}{x-1}+\frac{4}{y+1}=-2and\frac{3}{x-1}-\frac{1}{y+1}=7$

• A. (2, 0)
• B. (0, 2)
• C. $(\frac{3}{2},-2)$
• D. $(-\frac{3}{2},2)$

Answer 1

The correct option is C $(\frac{3}{2},-2)$

Let $\frac{1}{x-1}=aand\frac{1}{y+1}=b$

⇒ a + 4b = -2 ... (1)

3a - b = 7 ...... (2)

Multiplying equation (2) by 4, we get
12a - 4b = 28 .... (3)

Adding equation (1) and equation (3)
⇒ 13a = 26
a = 2

Solving for b, we get,
$b=-1$

$\therefore \frac{1}{x-1}=2\Rightarrow x-1=\frac{1}{2}$

$\Rightarrow x=\frac{3}{2}$

$\frac{1}{y+1}=-1\Rightarrow y+1=-1$

$\Rightarrow y=-2$