Solving Systems of Equations
By Elimination
Warm – up!!
*As you walk in, please pick up your
calculator!!*
Use substitution to solve the following
systems of equations.
1. x – 3 = y
2y + 7x = 4
2. 6x -8 = 3y
18 = 7y + 4x
Solving Systems of Equations
So far, we have solved systems using
graphing and substitution. Today we are
adding another tool to our toolbox called
ELIMINATION.
 Our goal for elimination is to cancel out
one of our variables so that we only
have one variable left to solve for.

Solving a system of equations by elimination.
Step 1: Put the equations in
Standard Form.
Step 2: Determine which
variable to eliminate.
Step 3: Eliminate the
variable and solve.
Step 4: Plug back in to find
the other variable.
Step 5: Check your
solution.
Standard Form: Ax + By = C
Look for variables that have the
same coefficient.
Solve for the variable.
Substitute the value of the variable
into the equation.
Substitute your ordered pair into
BOTH equations.
1) Solve the system using elimination.
2x + 2y = 6
3x – 2y = 4
Step 1: Put the equations in
Standard Form.
Step 2: Determine which
variable to eliminate.
They already are!
Look at my ys!
What coefficients do they both
have?
1) Solve the system using elimination.
2x + 2y = 6
3x – 2y = 4
Step 3: Eliminate the
variable and solve.
2x + 2y = 6
2x + 2y = 6
3x – 2y = 4 (+) 3x – 2y = 4
5x
= 10
x=2
Step 4: Plug back in to find
the other variable.
2(2) + 2y = 6
4 + 2y = 6
2y = 2
y=1
1) Solve the system using elimination.
2x + 2y = 6
3x – 2y = 4
Step 5: Check your
solution.
(2, 1)
2(2) + 2(1) = 6
3(2) - 2(1) = 4
A great way to know if you have
the right answer!!
2) Solve the system using elimination.
-4x + 4y = 7
4x – 3y = 9
Step 1: Put the equations in
Standard Form.
Step 2: Determine which
variable to eliminate.
They already are!
Which variable has the same
coefficient?
2) Solve the system using elimination.
-4x + 4y = 15
4x – 3y = 9
Step 3: Multiply the
equations and solve.
Eliminate one of the variables!
-4x + 4y = 15
-4x + 4y = 15
4x – 3y = 9 (+) 4x – 3y = 9
12y = 24
y=2
Step 4: Plug back in to find
the other variable.
x + 4(2) = 7
x+8=7
x = -1
2) Solve the system using elimination.
-4x + 4y = 15
4x – 3y = 9
Step 5: Check your
solution.
(-1, 2)
-4(-1) + 4(2) =15
4(-1) - 3(2) = 9
What is the first step when solving with
elimination?
Plug numbers into the equation.
Add or subtract the equations.
Solve for a variable.
Check your answer.
Determine which variable to eliminate.
Put the equations in standard form.
Put the steps of
solving by
elimination in
order!!
Which variable is easier to eliminate?
3x - 4y = 4
4x + 4y = 6
1.
2.
3.
4.
x
y
6
4
3) Solve the system using elimination.
You try!!
3x + 7y = -28
4x – 7y = 7
Step 1: Put the equations in
Standard Form.
They already are!
Step 2: Determine which
variable to eliminate.
What variable is
easiest to eliminate?
3) Solve the system using elimination.
3x + 7y = -28
4x – 7y = 7
Step 3: Multiply the
equations and solve.
Eliminate a variable!!!!
3x + 7y = -28
3x + 7y = -28
(+) 4x – 7y = 7
4x – 7y = 7
7x
= -21
x=-3
Step 4: Plug back in to find
the other variable.
3(-3) + 7y = -28
-9 + 7y = -28
7y = -37
y = -37/7
3) Solve the system using elimination.
3x + 7y = -28
4x – 7y = 7
Step 5: Check your
solution.
(-3, -37/7)
3(-3) + 7(-37/7) = -28
4(-3) - 7(-37/7) = 7
Solve using elimination.
2x – 3y = 1
-2x - 4y = 6
1.
2.
3.
4.
(2, 1)
(1, -2)
(5, 3)
(-1, -1)
You try!!