# Solve the simultaneous equation: 6x+y = 27 3x-2y = 6

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To work out simultaneous equations, the aim is to remove one letter from the equations, i.e. Remove the y's so you have only x's and numbers (or vice versa).

One way to do this is to get the coefficient in front of either the y's or x's to equal each other.

In this example, you can get the coefficients of the x's to equal each other if you multiply the second equation by two:

3x-2y = 6    (x2)

=   6x-4y = 12

So now..

6x+y = 27

6x-4y = 12

Since the coefficients equal each other, you can take one equation away from the other to remove the x's:

6x+y = 27

6x-4y = 12

------------

5y = 15           (y--4y = 5y, and 27-12 = 15)

Now solve y.

y = 15/5

y= 3

Now to find what x is, you put 3 in as y to either of the original equations:

6x+y = 27

6x+3 = 27

6x = 24

x = 4

There you go!

x=4 and y=3

to check you have the correct values, you can put the numbers back into the other equations. If the equation works you have it right.

3x-2y = 6

12-6 = 6

It works!

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