Download 3.2a: Solving Systems by Substitution File

Algebra 2 Honors
Name:
Section 3.2a: Solving Linear Systems: Substitution Method
Date:
The Substitution Method for Solving Systems of Equations:
In the previous section we were able to approximate the solution to a system by graphing each equation and see
where they crossed. Where they crossed was the point(s) (x,y) which made both equations true. It is oftentimes
a pain to graph (and not very accurate unless you use technology) so there are better and more accurate
algebraic ways to do so. The first method we will explore is known as the Substitution Method.
The Substitution Method:
Steps:
Example 1)
Solve the linear systems using the substitution method. I will demonstrate.
⎧3x − y − 13 = 0
⎨
⎩2x + 2y = −10
Example 2)
Solve the linear systems using the substitution method. I will demonstrate
⎧−x + 3y − 1 = 0
⎨
⎩4x + 6y − 8 = 0
Examples for you and your partner:
A) Solve by Substitution
⎧2x + 4 − y = 0
⎨
⎩4x + y = 8
B) Solve by Substitution
⎧2x + 3y = −1
⎨
⎩x − y + 3 = 0
Example 3) Let’s look at the last two examples on the previous notesheet. Solve using substitution.
⎧2x + 4y = 12
⎧x − y = 5
A. ⎨
B. ⎨
⎩x + 2y = 6
⎩2x − 2y = 9