I can solve a two variable system by substitution.
I can solve a two variable system by elimination.
The Substitution Method
 Step 1:
 Solve one of the equations for one of its variables.
 Step 2:
 Substitute the expression from Step 1 into the other
equation and solve for the other variable.
 Step 3:
 Substitute the value from Step 2 into the equation from
Step 1 and solve.
Which
equation is
easiest to get
a variable?
Example 1: Substitution
3x + 4y = -4
x + 2y = 2
 Step 1: solve for a
variable
x + 2y = 2
-2y -2y
x = 2 – 2y
 Step 3: Substitute the
value into Step 1
x = 2 – 2(5)
x = 2 – 10
x = -8
 Step 2: Substitute into
other equation
3x + 4y = -4
3(2 – 2y) +4y = -4
6 – 6y + 4y = -4
6 – 2y = -4
-6
-6
-2y = -10
-2
-2
y=5
Your turn to try.
3x – y = 13
2x + 2y = -10
The Elimination Method
 Step 1:
 Multiply one or both of the equations by a constant (#) to get
both a + and – coefficient for a variable.
 Step 2:
 Add the revised equation(s) from Step 1. By combining like
terms, one of your variables will eliminate. Solve for the
remaining variable.
 Step 3:
 Substitute the value from Step 2 into either original equation
and solve for the other variable.
Example 2:
Elimination (Multiplying 1 Equation)
2x – 4y = 13
4x – 5y = 8
Which
variables are
multiples of
each other?
 Step 1: Multiply to get
a + and – variable.
-2(2x – 4y = 13)
-4x + 8y = -26
 Step 2: Add the
revised equation and
combine like terms.
-4x + 8y = -26
4x – 5y = 8
3y = -18
3
3
y = -6
Continued….
2x – 4y = 13
4x – 5y = 8
 Step 3: Substitute into
an original equation to
solve for the other
variable.
 y = -6
2x – 4y = 13
2x – 4(-6) = 13
2x + 24 = 13
-24
-24
2x = -11
2
2
x=
−11
2
Example
3:
Elimination
and multiply it by
(Multiplying 2 Equations)
Choose a variable
the variable in the
other equation.
7x – 12y = -22
-5x + 8y = 14
Step 1: Multiply to get
the same + and –
variable.
5(7x – 12y = -22)
35x – 60y = -110
7(-5x + 8y = 14)
-35x + 56y = 98
Step 2: Combine like terms
35x – 60y = -110
-35x + 56y = 98
-4y = -12
-4 -4
y=3
Continued…
7x – 12y = -22
-5x + 8y = 14
y=3
Step 3: Substitute into
an original equation
7x – 12y = -22
7x – 12(3) = -22
7x – 36 = -22
+36 +36
7x = 14
7 7
x=2
Table Partner Classwork
 Textbook
 Pg 153

35-40
 When you are finished,
check with me.
 Start on homework.
 Homework
Solve the system using a
chosen method.
1.
x + 5y = 33
4x + 3y = 13
2. -2x + 3y = -13
6x + 2y = 28