Solve the simultaneous equations 2x + 3y = 4, 3x + 6y = 3

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Label the equations
(1): 2x + 3y = 4
(2): 3x + 6y = 3

We need the same number of x's or y's in the equations, so multiply (1) by 3 and (2) by 2
giving (3): 6x + 9y = 12
(4): 6x + 12y = 6

Subtract (3) from (4)
6x + 12y - 6x - 9y = 6 - 12
so 3y= -6
so y= -2

Substitute the y value into (1) to find x
2x + (3*-2) = 4
        2x - 6 = 4
             2x = 10
               x = 5

Check by substituting into (2)
(3*5) + (6*-2) = 15 - 12 = 3 the solutions work

So x = 5 and y = -2

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