The values of ‘x’ and ‘y’ if 5/y - 2/x = 7/6 and 36/x - 24/y

1.	The values of ‘x’ and ‘y’ if 5/y - 2/x = 7/6 and 36/x - 24/y = 1 is ..........A) x = 4, y = 3 B) x = -4, y = 3 C) x = -4, y = -3 D) x = 4, y = -3
Answer» 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. Correct option is A) x = 4, y = 3

The values of ‘x’ and ‘y’ if 5/y - 2/x = 7/6 and 36/x - 24/y = 1 is ..........A) x = 4, y = 3 B) x = -4, y = 3 C) x = -4, y = -3 D) x = 4, y = -3

Answer»

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.

Correct option is A) x = 4, y = 3