Question

If (x, y) is the solution of system of linear equations $\frac{2}{x}+\frac{3}{y}=5,\frac{5}{x}-\frac{6}{y}=-1,$ then the value of (2x – y) is equal to

• A. 2
• B. 4
• C. 1
• D. -1

Answer 1

The correct option is C 1

Given $\frac{2}{x}+\frac{3}{y}=5and\frac{5}{x}-\frac{6}{y}=-1$
Pair of given linear equations can be written as:

2 +3 = 5 and 5 + 6 = -1

Now, let $\frac{1}{x}=pand\frac{1}{y}=q.$

Then, the equations become,
2p + 3q = 5 ..…(i)
and, 5p – 6q = –1 .....(ii)

Multiplying (i) by 2 and adding to (ii) we get,
2 (2p) + 2 (3q) + 5p - 6q = 2(5) - 1

$4p+6q+5p-6q=10-19p=9p=1$

Substituting the value of p in (i), we get

2 × 1 + 3q = 5
⇒ 2 + 3q = 5
⇒ q = 1
Thus, p = 1 and q = 1.

$[Qx=\frac{1}{p}andy=\frac{1}{q}]$

∴ x = 1 and y = 1
So, 2x – y = (2 × 1) – 1 = 1
Hence, the correct answer is option (3).