# 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.
$\frac{7}{2x + 1} + \frac{13}{y + 2} = 27 ; \frac{13}{2x + 1} + \frac{7}{y + 2} = 33$

#### 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?

#### 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