Solve for x and y:

$2 x + 3 y = 0, 3 x + 4 y = 5.$

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Solution

$2 x + 3 y = 0$ -----(1)

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

From equation (1)

$2 x + 3 y = 0$

$2 x = - 3 y$

$x = \frac{- 3 y}{2}$ ......(3)

Put the value of x in (2)

$3 x + 4 y = 5$

$3 (\frac{- 3 y}{2}) + 4 y = 5$

$\frac{- 9 y}{2} + 4 y = 5$

$\frac{- 9 y}{2} + \frac{8 y}{2} = 5$

$- 1 y = 10$

$y = - 10$

sub y in 1

$2 x + 3 y = 0$

$2 x + 3 (- 10) = 0$

$2 x - 30 = 0$

$x = \frac{30}{2} = 15$

So $x = 15$ and $y = - 10$

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