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Elimination Method of Finding Solution of a Pair of Linear Equations

If x : y = ...

Question

If $x : y = 3 : 4$ find $7 x - 4 y : 3 x + y$ is

5 : 13

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5 : 4

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13 : 5

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14 : 5

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Solution

The correct option is B $5 : 13$
$x : y = 3 : 4$ $7 x - 4 y : 3 x + y$
$\frac{x}{y} = \frac{3}{4}$ Let $x = 3 k, y = 4 k$
$\frac{7 x - 4 y}{3 x + y} = \frac{7 (3 k) - 4 (4 k)}{3 (3 k) + 4 k}$
$= \frac{21 k - 16 k}{9 k + 4 k} = \frac{5 k}{13 k}$
$= \frac{5}{13}$ .

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