Addition Method of Solving Equations
The Addition Method of solving equations is sometimes
also called the Elimination Method. Both however do the
same thing and use the properties of Addition.
1. Decide which variable is going to cancel out.
2. What needs to be done to one or both of the equations to
make that variable cancel out?
3. Remember that for the variable to cancel both must be the
same number and one need to be positive and the
other negative.
4. Multiply the entire equation by the correct number and
also multiply the other entire equation if need to.
5. Add the two equations together canceling out one variable
and then solve for the other variable.
6. Once you solved for one variable plug value back into one
of the equations to solve for the other.
Example:
3x+y=5
6x-y=4
3x+y=5
6x-y=4
9x+0=9
9x=9
x=1
Set up the equations and
decide which variable will
cancel.
The y’s already cancel so
there is no need to multiply
the top or bottom equation
by anything.
Combine together and
solve for x.
Divide by 9 on both sides.
3x+y=5
3+y=5
Now pick an equation that
contains both the (x) and
(y). Plug in the value for (x)
and solve for (y).
y=2
Answer: (1,2)
3(1)+y=5
Example:
3x+y=-11
6x-2y=-2
3x+y=-11
6x-2y=-2
2(3x+y=-11)
Set up the equations and
decide what variable will
cancel out.
The (y) variable is going to
be the easiest to cancel.
Multiply the entire first
equation by 2 so that the
(y) will cancel.
6x+2y=-22
6x+2y=-22
6x-2y= -2
12x+0=-24
12x=-24
The top equation now turns
into. 6x+2y=-22
Replace the old top
equation with the new one.
Combine the two equations
together.
Solve for (x).
x=-2
3x+y=-11
3(-2)+y=-11
Divide both sides by 12.
Now go back and pick an
equation that contains both
an (x) and (y) and plug 12
in for (x) and solve for (y).
-6+y=-11
Answer: (12,-5)
y=-5
Example:
x+5y=18
3x+2y=-11
x+5y= 18
3x+2y=-11
-2( x+5y= 18)
5(3x+2y=-11)
-2x- 10y=-36
15x+10y=-55
13x+ 0= -91
Set the equation up and
decide which variables will
cancel. In this case pick the
(y) to cancel.
The lowest common
multiple for the 5 and 2 is
10. Remember one must
be negative and the other
positive.
Multiply the top by -2 and
the bottom by 5.
Now combine the two new
equations together.
Solve for (x).
13x=-91
x+5y=18
Now pick an equation that
has both an (x) and (y) in it
and plug in (-7) in for (x)
and solve for (y).
-7+5y=18
Answer: (-7,5)
x=-7
5y=25
y=5
Updated 2-16-09