7.2
Solving Linear Systems by
Substitution
Solving a system of linear equations…
You’ve already learned:
1. Graphing
We have to learn:
2. Substitution
3. Elimination
Objectives for Today:
1. Solve a system of equations by substitution
2. Solve systems from the real world
Solve the System by Substitution
Here’s Our Steps:
Solve a system by substitution:
1. Solve for one of the variables and star it.
 Hint: Look for the variable that is already alone OR easy to isolate.
2. Substitute this expression into the other equation.
3. Solve for the only variable.
4. Substitute this value into the starred equation.
5. Clearly state your answer as an ordered pair.
6. Check the answer.
When we say to solve for one variable…Which is the best
variable to use for substitution?
-3x  y  9

2x + 4y  8
x  3y  -11

2x  5y  33
ì x - 3y = 0
í
î x - 2y =10
Example 1
Solve the System by Substitution
Solve the system by substitution.
- x  y  1

2x  y  2
(-1, 0)
Solve a system by substitution:
1. Solve for one of the
variables and star it.
2. Substitute this expression
into the other equation.
3. Solve for the only variable.
4. Substitute this value into the
starred equation.
5. Clearly state your answer as
an ordered pair.
6. Check the answer.
Example 2
Solve the System by Substitution
Solve the system by substitution.
3x  2y  14

5x  y  6
(2, 4)
Solve a system by substitution:
1. Solve for one of the
variables and star it.
2. Substitute this expression
into the other equation.
3. Solve for the only variable.
4. Substitute this value into the
starred equation.
5. Clearly state your answer as
an ordered pair.
6. Check the answer.
Example 3
Solve the System by Substitution
Solve the system by substitution.
5x  4y  37

x  3y  3
(9, 2)
Solve a system by substitution:
1. Solve for one of the
variables and star it.
2. Substitute this expression
into the other equation.
3. Solve for the only variable.
4. Substitute this value into the
starred equation.
5. Clearly state your answer as
an ordered pair.
6. Check the answer.
Example 4
Solve the System by Substitution
Solve the system by substitution.
6x  2y =16

-2x + y = -2
(2, 2)
Solve a system by substitution:
1. Solve for one of the
variables and star it.
2. Substitute this expression
into the other equation.
3. Solve for the only variable.
4. Substitute this value into the
starred equation.
5. Clearly state your answer as
an ordered pair.
6. Check the answer.
Example 5
Real Life Linear System
In one day, the Baseball Hall of Fame
in Cooperstown admits 321 adults and
children and collects $1590. The price
of admission is $6 for an adult and $4
for a child. How many adults and how
many children were admitted to the
museum that day.
153 adults & 168 children
Exit Slip
To be completed before leaving…
Solve the system of equations by substitution.
-4x + y = -10

6x + 2y = 22
7.2
Practice
Worksheet
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