# Solve the Following Simultaneous Equations. 2 X + 2 3 Y = 1 6 ; 3 X + 2 Y = 0 - Algebra

Solve the following simultaneous equations.
$\frac{2}{x} + \frac{2}{3y} = \frac{1}{6} ; \frac{3}{x} + \frac{2}{y} = 0$

#### Solution

$\frac{2}{x} + \frac{2}{3y} = \frac{1}{6} ; \frac{3}{x} + \frac{2}{y} = 0$
Let $\frac{1}{x} = u\text{ and }\frac{1}{y} = v$
$2u + \frac{2}{3}v = \frac{1}{6}$
$12u + 4v = 1 . . . . . \left( I \right)$
$3u + 2v = 0 . . . . . \left( II \right)$
Multiply (II) with 2
$6u + 4v = 0 . . . . . \left( III \right)$
$\left( I \right) - \left( III \right)$
$6u = 1$
$\Rightarrow u = \frac{1}{6}$
Putting the value of in II.
$3 \times \frac{1}{6} + 2v = 0$
$\Rightarrow \frac{1}{2} + 2v = 0$
$\Rightarrow v = \frac{- 1}{4}$
$\frac{1}{x} = u$
$\Rightarrow x = 6$
$\frac{1}{y} = v$
$\Rightarrow y = - 4$
$\left( x, y \right) = \left( 6, - 4 \right)$
Concept: Graphical Method of Solution of a Pair of Linear Equations
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#### APPEARS IN

Balbharati Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board
Chapter 1 Linear Equations in Two Variables
Problem Set 1 | Q 6.1 | Page 28