UNIT 3: SYSTEMS OF LINEAR EQUATIONS & INEQUALITIES
MA40: ALGEBRA II
3.1a – Solve Linear Systems by SUBSTITUTION METHOD
(Text Ref: Ch 3.2 Pg 148-155)
AZ Standards: HS.A-REI.5, HS.A-REI.6, HS.A-REI.7, HS.A-REI.11
Objective: TSWD synthesis of linear equations by combining their understanding of solutions
and graphs in solving systems of two equations.
Vocabulary
System of Two
Linear Equations
Solution
I. Vocabulary
System of Two Linear Equations –
Solution to a System of Linear Equations –
II. Solutions to Systems of Linear Equations
Check Solutions
A. Checking Solutions of a Linear System
Check whether the ordered pair are solutions to the system.
1) 3 x  2 y  3
3x  y  3
1
3


a)  , 2  and b) 1,3
Number of Solutions
for a System of
Linear Equations
The
Substitution Method
2)
x  2 y  7
2x  3y  0
a)  1, 5 and b)  3, 2
B. Number of Solutions for a System of Linear Equations
III. Solving a System by Substitution Method
A. The Substitution Method
Step 1 –
Step 2 –
Step 3 –
3.2a – Solve Linear Systems by Substitution Method (continued)
Solve the
System
B. Solve the system
1)  x  y  2
2x  y  7
2) 3x  4 y  4
3)
x  2y  2
2 x  4 y  12
x y 2
IV. Systems with Many or No Solutions
A. Interpret the result. Without graphing, classify each system as independent (1-solution),
dependent (infinite solutions), or inconsistent (no solutions).
1) 3 x  y  5
15 x  5 y  2
2) y  2 x  3
4 x  2 y  6
3) x  y  5
y  3  2x