Solve the following pair of equations by reducing them to a pair of linear equations:
$\frac{2 x - 3 y}{x y} = 4$ and $\frac{15 x + 3 y}{x y} = 30$

x = - 1, y = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = 1, y =\propto

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = 0, y = 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x =\propto, y = \frac{1}{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is C $x =\propto, y = \frac{1}{2}$
Simplify the equations,
$\frac{2 x}{x y} - \frac{3 y}{x y} = 4$ ; $\frac{15 x}{x y} + \frac{3 y}{x y} = 30$
$\frac{2}{y} - \frac{3}{x} = 4$ ; $\frac{15}{y} + \frac{3}{x} = 30$
Assume $\frac{1}{x} = a; \frac{1}{y} = b$
$2 b - 3 a = 4$ ----- (1)
$15 b + 3 a = 30$ ---- (2)
___________
$17 b = 34$
$b = \frac{34}{17} = 2$
Put the value of b in eqn (1)
$2 (2) - 3 a = 4$
$4 - 4 = 3 a$
$0 = 3 a$
$a = 0$
$∴ \frac{1}{x} = a; \frac{1}{y} = b$
$x =\propto, y = \frac{1}{2}$
$∴$ the solution is $(x =\propto, y = \frac{1}{2})$

Suggest Corrections

Similar questions

\frac{x + y}{x y} = 2, \frac{x - y}{x y} = 6

\frac{1}{2 x} + \frac{1}{3 y} = 2; \frac{1}{3 x} + \frac{1}{2 y} = \frac{13}{6}

\frac{2}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 2; \frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = - 1

\frac{4}{x} + 3 y = 14; \frac{3}{x} - 4 y = 23

\frac{5}{x - 1} + \frac{1}{y - 2} = 2; \frac{6}{x - 1} - \frac{3}{y - 2} = 1

\frac{7 x - 2 y}{x y} = 5; \frac{8 x + 7 y}{x y} = 15

6 x + 3 y = 6 x y; 2 x + 4 y = 5 x y

\frac{10}{x + y} + \frac{2}{x - y} = 4; \frac{15}{x + y} - \frac{5}{x - y} = - 2

\frac{1}{3 x + y} + \frac{1}{3 x - y} = \frac{3}{4}; \frac{1}{2 (3 x + y)} - \frac{1}{2 (3 x - y)} = \frac{- 1}{8}

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

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

Solve the following pair of linear equations graphically: 2x+3y=2 and x-y=1

\frac{2}{\sqrt{x}} + \frac{2}{\sqrt{y}} = 2

\frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = - 1

Join BYJU'S Learning Program