Question

Solve the following pair of equations

$\frac{5}{x-1}+\frac{1}{y-2}=2$

$\frac{6}{x-1}-\frac{3}{y-2}=1$

• A. 4,5
• B. 5,3
• C. $\frac{1}{3}$, $\frac{1}{3}$
• D. None of these

Answer 1

The correct option is A

4,5

substitute $\frac{1}{x-1}$ as p and $\frac{1}{y-2}$ as q in the given equations.

$5p+q=2$.......(1)

$6q-3q=1$.......(2)

Now we can solve the pair of equation by method of elimination.

Multiply the first equation by 3.We get,

$15p+3q=6$

$6p-3q=1$

Adding the above equations

$21p=7$

$p=\frac{1}{3}$

Substituting $p=\frac{1}{3}$ in one of the equations, we get $q=\frac{1}{3}$

As we have assumed $p=\frac{1}{x-1}$

Therefore, $\frac{1}{x-1}=\frac{1}{3}$

$\Rightarrow x=4$

Similarly we assumed $q=\frac{1}{y-2}$

$\frac{1}{y-2}=\frac{1}{3}$

$\Rightarrow y-2=3$

$\Rightarrow y=5$

Thus $x=4,y=5$