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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.

\[\frac{148}{x} + \frac{231}{y} = \frac{527}{xy} ; \frac{231}{x} + \frac{148}{y} = \frac{610}{xy}\]
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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)
\[2 - x = 1\]
\[ \Rightarrow x = 1\]
\[\left( x, y \right) = \left( 1, 2 \right)\]
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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 6.3 | Page 28
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