# Solve the Following Simultaneous Equations. 148 X + 231 Y = 527 X Y ; 231 X + 148 Y = 610 X Y - Algebra

Solve the following simultaneous equations.

$\frac{148}{x} + \frac{231}{y} = \frac{527}{xy} ; \frac{231}{x} + \frac{148}{y} = \frac{610}{xy}$

#### Solution

$\frac{148}{x} + \frac{231}{y} = \frac{527}{xy} ; \frac{231}{x} + \frac{148}{y} = \frac{610}{xy}$
Multiply by xy
$148y + 231x = 527 . . . . . \left( I \right)$
$231y + 148x = 610 . . . . . \left( II \right)$
$\text{ Adding }\left( I \right)\text{ and }\left( II \right)$
$379y + 379x = 1137$
$\Rightarrow x + y = 3 . . . . . \left( III \right)$
$\left( II \right) - \left( I \right)$
$83y - 83x = 83$
$\Rightarrow y - x = 1 . . . . . \left( IV \right)$
$\left( III \right) + \left( IV \right)$
$2y = 4$
$\Rightarrow y = 2$
Putting the value of y in (IV)
$2 - x = 1$
$\Rightarrow x = 1$
$\left( x, y \right) = \left( 1, 2 \right)$
Is there an error in this question or solution?

#### APPEARS IN

Balbharati Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board
Chapter 1 Linear Equations in Two Variables
Problem Set 1 | Q 6.3 | Page 28