Choose the correct answer in each of the following questions:

If $2 x + 3 y = 12 a n d 3 x - 2 y = 5$ then

(a) x=2,y=3 (b) x=2,y=-3 (c) x=3,y=2 (d) x=3,y=-2

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Solution

$2 x + 3 y = 12$ ....(1)

$3 x - 2 y = 5$ ......(2)

From equation (1) $3 y = - 2 x + 12$

$y = \frac{- 2 x}{3} + 4$

Put this in for variable y in equation [2]

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

$\frac{13 x}{3} = 13$

$13 x = 39$

$x = 3$

put in equation (1)

$2 (3) + 3 y = 12$

$6 + 3 y = 12$

$3 y = 12 - 6$

$y = \frac{6}{3}$

$y = 2$

$(x, y) = (3, 2)$

Answer (c) $x = 3, y = 2$

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