Solve the following system of equations by Paravartya method of Vedic mathematics:
$2 x + y = 5, 3 x - 4 y = 2$

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Solution

$2 x + y = 5....... (1)$
$3 x - 4 y = 2...... (2)$
Here $a_{1} = 2, b_{1} = 1, c_{1} = 5$
$a_{2} = 3, b_{2} = - 4, c_{2} = 2$
By Parvartya method of Vedic mathematics
$x = \frac{b_{1} c_{2} - b_{2} c_{1}}{a_{2} b_{1} - a_{1} b_{2}}$
$= \frac{1 \times 2 - (- 4) \times 5}{3 \times 1 - 2 \times (- 4)} = \frac{2 + 20}{3 + 8} = \frac{22}{11} = 2$
$x = 2$
$y = \frac{c_{1} a_{2} - c_{2} a_{1}}{d e n o m i n a t o r}$
$\frac{5 \times 3 - 2 \times 2}{11} = \frac{15 - 4}{11} = \frac{11}{11}$
$y = 1$
$x = 2, y = 1$

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