Solve the simultaneous equations: 4x+y=25 and x-3y=16

Lets first give the equations names.

4x+y=25 (A)

x-3y=16 (B)

We want to get the equations so that they have either the same number of x's or same number of y's. So let's multiply equation (A) by three so that both equations have 3y in them.

(A) x 3: 12x+3y=75

STOP (Same signs, Take-away. Opposite signs, Plus).

So our 3y's have opposite signs [(A) is +3y and (B) is -3y)] so we need to add these equations together to eliminate all of the y's.

(A) + (B) gives 13x=91

x=91/13, So x=7

We now need to subsitute our value for x into one of the equations to find y.

So subbing x=7 into equation (B) gives:

7-3y=16

7-16=3y

-9=3y

y=-3

So our solution is x=7, y-3.

We can now check our solution by subbing these values into the other equation. So subbing x=7 and y=-3 into (A) gives 4(7)+(-3)=25. This means our solution for the simultaneous equation is correct because these values also work for equation (A).