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Solve the Following Simultaneous Equations. 7 2 X + 1 + 13 Y + 2 = 27 ; 13 2 X + 1 + 7 Y + 2 = 33 - Algebra

Solve the following simultaneous equations.
\[\frac{7}{2x + 1} + \frac{13}{y + 2} = 27 ; \frac{13}{2x + 1} + \frac{7}{y + 2} = 33\]

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Solution

\[\frac{7}{2x + 1} + \frac{13}{y + 2} = 27 ; \frac{13}{2x + 1} + \frac{7}{y + 2} = 33\]
\[\frac{1}{2x + 1} = u\text{ and }\frac{1}{y + 2} = v\]
\[7u + 13v = 27 . . . . . \left( I \right)\]
\[13u + 7v = 33 . . . . . \left( II \right)\]
(I) + (II)
\[20u + 20v = 60\]
\[u + v = 3 . . . . . \left( III \right)\]
(II) − (I)
\[6u - 6v = 6 \]
\[u - v = 1 . . . . . \left( IV \right)\]
(III) + (IV)
\[2u = 4\]
\[ \Rightarrow u = 2\]
Putting the value of u in (IV) 
\[2 - v = 1\]
\[ \Rightarrow v = 1\]
\[\frac{1}{2x + 1} = u = 2 \]
\[ \Rightarrow 2x + 1 = \frac{1}{2}\]
\[ \Rightarrow x = \frac{- 1}{4}\]
\[\text{ and }\frac{1}{y + 2} = v = 1\]
\[ \Rightarrow y + 2 = 1\]
\[ \Rightarrow y = - 1\]
\[\left( x, y \right) = \left( \frac{- 1}{4}, - 1 \right)\]
  Is there an error in this question or solution?
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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 6.2 | Page 28
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