Question

Solve the following pair of equation

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

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

• A. 4,5
• B. 5,3
• C. 1/3, 1/3
• D. None of these

Answer 1

The correct option is A

4,5

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

5p+q=2

6q-3q=1

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

15p+3q=6

6p-3q=1

Adding both

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

Now by substituting the value in one of the equation we find q= $\frac{1}{3}$

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

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

→ x = 4

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

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

→ y - 2 = 3

→ y = 5

Thus x=4, y=5