Chapter 3 – Systems of
Linear Equations
3.3 – Solving Systems by
Linear Combination
3.3 – Solving Systems by Linear
Combination
Today we review:
– Solving a system of linear equations in two
variables by the linear combination method.
3.3 – Solving Systems by Linear
Combination
Linear combination of two equations –
An equation obtained by multiplying one or
both sides by a constant and adding the
resulting equations
3.3 – Solving Systems by Linear
Combination
If needed, multiply one or both sides by a
constant so the coefficients for one of the
variables are opposites
Add the equations from step 1. This will
eliminate one variable. Solve for the other
variable
Substitute the value from step 2 into
either equation and solve for the other
variable
3.3 – Solving Systems by Linear
Combination
Example 1
– Solve the linear system using the linear
combination method.
8x + 2y = 4
-2x + 3y = 13
3.3 – Solving Systems by Linear
Combination
Example 2
– Solve the system using the linear combination
method.
3x + 2y = -3
-6x – 5y = 12
3.3 – Solving Systems by Linear
Combination
Example 3
– Solve the system using the linear combination
method
2x – 3y = 4
6x – 9y = -3
3.3 – Solving Systems by Linear
Combination
Example 4
– You and your friend go to a theme park. Your
cost for the entry fee and 7 rides is $22. Your
friend’s cost for the entry fee and 9 rides is
$26. What is the cost of the entry fee and of
each ride?