# Solve the following simultaneous equation: 3x+2y=20 and x+4y=20

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In this example, we want to find values for both x and y which are our unknowns.

So we start by rearranging x to be on its own but still in terms of y. We then can plot it into the next equation.

Hence we get the following equations:

.  x=20-4y (See, 4y has been taken over to the other side and hence the sign changes)

.  3x+2y=20

Then we substitute this new value of x in the other equation:

3(20-4y)+2y=20

60-12y+2y=20 (we have multiplied out the 3 and its bracket to simplify)

-10y=20-60 (make sure you change the sign when taking the 60 across!)

-10y=-40

-y=-4 (here we divided 40 by 10)

y=4 (the minus signs cancel each other out)

Now that you've found y we must plot it back into the original equation to find x:

x+4y=20

x+4(4)=20

x+16=20

x=20-16

x=4

Therefore, x=4 and y=4.

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