Find the solution of the given pair of equations
$2 x + 3 y = 9, 3 x + 4 y = 5$

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Solution

Given,

$2 x + 3 y = 9$ ...(1)

$3 x + 4 y = 5$ ...(2)

Multiply equation (1) with 3

$6 x + 9 y = 27$ ...(3)

Multiply equation (2) with 2

$6 x + 8 y = 10$ ...(4)

Subtracting (4) from (3):

$y = 17$

Substituting $y = 17$ in (1), we get

$2 x + 3 (17) = 9$

$\Rightarrow 2 x = 9 - 51 = - 42 \Rightarrow . x = \frac{- 42}{2} = - 21$

$∴ x = - 21, y = 17$

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