Solve the equations using elimination method:
$2 x + 3 y = 12$ and $4 x + 2 y = 8$

(0, 5)

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(-1, 5)

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(0, 4)

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(-5, 0)

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Solution

The correct option is C (0, 4)
$2 x + 3 y = 12$ ----- (1)
$4 x + 2 y = 8$ ----- (2)
Multiply equation (1) by 4 and then subtract the equation (3) and (4)
$4 x + 12 y = 48$ ----- (3)
$4 x + 2 y = 8$ ----- (4)
(-) (-) (-)
___________
$10 y = 40$
$y = \frac{40}{10} = 4$
Put the value of y in equation (1), we get
$2 x + 3 y = 12$
$2 x + 3 (4) = 12$
$2 x = 1212$
$2 x = 0$
$x = \frac{0}{2} = 0$
Therefore the solution is (0, 4)

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