Systems of Equations and
Inequalities in Two Variables
A-REI.3; A-REI.5; A-REI.6; A-REI.7
Table of Contents
28: Guided
Practice
29: How Do I
Solve Systems of
Equations with
Elimination?
EQ: How Do I Solve Systems of
Equations with Elimination?
3/18/2016
System of
Equations
A collection of 2 or more
lines, including
nonlinear equations
Elimination One variable is
Method
eliminated by adding or
subtracting the two
equations of the system
to obtain a single
equation in one variable
1. Add or subtract the
equations to eliminate one
variable.
2. Solve the resulting
equation for the other
variable
3. Substitute the value into
the original equation to find
the value of the eliminated
variable.
One
Solution
The two lines cross each
other in exactly one point
on the graph
x=a
The two lines on the graph
Infinite
Solutions lie on top of each other.
a=a
No
Solution
The two lines never cross.
a=b
Example 1:
Use
elimination to
solve the
system of
equations
2x – 3y = 12
x + 3y = 6
2x
–
3y
=
12
+
+
+
____________
x + 3y = 6
__
3x = 18
__
3
3
x=6
x + 3y = 6
6+ 3y = 6
__________
-6
-6
3y = __
0
__
3
3
y=0
Solution: (6, 0)
Guided Practice 1
Using the elimination method, solve
the system of equations
2x + 2y = -2
3x – 2y = 12
Guided Practice 2
Using the elimination method, solve
the system of equations
6x + 5y = 4
-6x + 7y = 20
Guided Practice 3
Using the elimination method, solve
the system of equations
x + y = -1
x–y=7
Questions
You’ve already found the x-value. Does
it matter which equation you use to find
the y-value? Why?
How could you check your answer?
How do you know which variable to
eliminate first?
Example 2:
Use
elimination to
solve the
system of
equations
3x + 3y = 6
3x – y = -6
3x + 3y = 6
–
–
–
3x – y = -6
____________
__
4y = 12
__
4
4
y=3
3x – y = 6
3x – 3 = -6
__________
+3 +3
3x =__
-3
__
3
3
x = -1
Solution: (-1, 3)
Guided Practice 4
Using the elimination method, solve
the system of equations
6x – 3y = 6
6x + 8y = -16
Guided Practice 5
Using the elimination method, solve
the system of equations
4x + 3y = 19
6x + 3y = 33
Guided Practice 6
Using the elimination method, solve
the system of equations
2x + 6y = 17
2x – 10y = 9
Questions
How can you decide whether to add or
subtract to eliminate a variable in a
system of equations?
What do you think would happen if you
couldn’t add or subtract while using the
elimination method? Do you think there
would be a way to solve the problem?
Example 3:
Use
elimination to
solve the
system of
equations
2x + 10y = 2
3x – 5y = -17
2x + 10y = 2
2(
3x – 5y = -17 )
______________
2x + 10y = 2
+ +
+
6x – 10y = -34
______________
__
__
8x = -32
8
8
x = -4
2x + 10y = 2
2(-4) + 10y = 2
-8 + 10y = 2
______________
+8
+8
__ = 10
__
10y
(-4, 1)
10
10 y = 1
Guided Practice 7
Using the elimination method, solve
the system of equations
x – 3y = 4
-5x + 15y = -20
Guided Practice 8
Using the elimination method, solve
the system of equations
9x + y = 9
3x – 2y = -11
Guided Practice 9
Using the elimination method, solve
the system of equations
x – 3y = 4
-5x + 15y = -20
Questions
Do you think you could multiply the top
and bottom by different numbers to
solve systems with elimination? Why
or why not?
When you solve a system by
elimination, how can you tell if there is
zero, one, or infinite solutions?
Classwork/Homework
For classwork/homework, please do the
worksheet provided. It will be due on
Monday.
Solving solutions and answers are on
the class website 