Correct option is (A) x = 4, y = 3
Take \(\frac1x=X\;\&\;\frac1y=Y\) then given equations are convert into
5Y - 2X \(=\frac76\) __________(1)
and 36X - 24Y = 1 __________(2)
Multiply equation (1) by 18, we get
90Y - 36X = 21 __________(3)
By adding equations (2) & (3), we get
(36X - 24Y) + (90Y - 36X) = 1+21
\(\Rightarrow\) 90Y - 24Y = 22
\(\Rightarrow\) 66Y = 22
\(\Rightarrow\) Y = \(\frac{22}{66}=\frac13\)
\(\therefore y=\frac1Y=3\) \((\because Y=\frac1y)\)
Then from (1),
2X = 5Y - \(\frac76\)
\(=\frac{5}{3}-\frac{7}{6}=\frac{10-7}{6}\)
\(=\frac36=\frac12\)
\(\therefore X=\frac14\)
\(\Rightarrow\) x = 4 \((\because X=\frac1x)\)
Hence, x = 4 & y = 3 is the solution of given system of equations.
