Question

Solve the following pair of equations.
$\frac{5}{x-1}+\frac{1}{y-2}=2$ $\frac{6}{x-1}-\frac{3}{y-2}=1$ Here, x $\ne$ 1 and y $\ne$ 2

Choose the correct answer from the given options.

• A.
  $(4,5)$
• B.
  $(3,2)$
• C.
  $(1,0)$
• D.
  $(-3,2)$

Answer 1

The correct option is A

$(4,5)$
If we substitute $\frac{1}{x-1}$ as P and $\frac{1}{x-2}$ as q in the given equations, we get the equations as

$5p+q=\mathrm{2...}\left(1\right)6p-3q=\mathrm{1...}\left(2\right)$

Now, we can solve the pair of equations by method of elimination.

On multiplying the first equation by 3 and then adding it to (2), we get

$15p+3q=66p-3q=1-------p=\frac{1}{3}$

Now by substituting the value of p inequation (2) we get

$q=\frac{1}{3}Now,p=\frac{1}{x-1}\Rightarrow \frac{1}{x-1}=\frac{1}{3}\Rightarrow x=4Similarlyweassumedq=\frac{1}{y-2}\Rightarrow \frac{1}{y-2}=\frac{1}{3}\Rightarrow y-2=3\Rightarrow y=5\therefore x=4andy=5$