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

We need to have either the same number of x's or the same number of y's in each equation so that we can add or subtract them to be left with just x or just y. We can do this by multiplying the second equation by 4:

4x - 12y = 64

Now both equations have "4x" in them, so if we subtract one from the other we will get rid of the x's and be left with just y's.

                4x + y = 25

MINUS     4x - 12y = 64

EQUALS         13y = -39

We then divide both sides of the equation to find what y equals:

y = -39/13 = -3

Now we substitute our value for y back into one of the equations to find what x is.

x - 3(-3) = 16

x + 9 = 16

x = 16 - 9 = 7

We can check our answers by substituting both the x and y values into the two equations. If the equations both balance then our answers are correct!