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Neuron
If you would like to solve the system of equations 5x + 4y = 12 and 3x - 3y = 18 using elimination, you can do this using the following steps:

5x + 4y = 12    /*3
3x - 3y = 18    /*4
_____________
15x + 12y = 36
12x - 12y = 72
_____________
15x + 12y + 12x - 12y = 36 + 72
15x + 12x = 36 + 72
27x = 108
x = 108/27
x = 4

3x - 3y = 18
3 * 4 - 3y = 18
12 - 3y = 18
12 - 18 = 3y
3y = -6
y = -6/3
y = -2

(x, y) = (4, -2)

The correct result would be: x = 4 and y = -2.
meerkat18
From the second equation,
                                  3x = 18 + 3y    ; x = 6 + y
Substitute this expression for x to the x of the first equations. Thus,
                                 5(6 + y) + 4y = 12
The value of y from this equation is -2. 
Going back to the expression for x, x = 6 + y = 6 - 2 = 4. Thus, the solution to this system is (4, -2). 

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