Nov. 2, 2010
Lori Simonelli
Text: Prentice Hall, Algebra II
Chapter 3 Linear Systems
Section 3-2 Solving Systems Algebraically
Obj. 1 Students will be able to solve systems by substitution.
Obj. 2 Students will be able to solve systems by elimination.
Standards: 2.8.11.D,E,F,G,H
PSSA/SAT Warmup: PSSA Momentum page 29.
Motivation: United Streaming video.
Overview: Solving a system of linear equations algebraically by using substitution or
elimination. Substitution will be used when you have a coefficient of 1 or -1.
Elimination will be used when you can easily find opposites.
Substitution used when you have a coefficient of 1 or -1.
The substitution method is used to
eliminate one of the variables by
replacement when solving a system
of equations.
Think of it as "grabbing" what one
variable equals from one equation and
"plugging" it into the other equation.
Example 1: 2x - 3y = 6
x + y = -12
1: Solve one of the equations for "y =" or "x ="
2: Grab the new equation and plug it into the
other equation.
3: Solve for the unknown variable.
4: Plug that answer into the original equation
and solve for the remaining variable.
5: Check: plug solution into BOTH equations,
they should both be TRUE.
Example 2: 3x - y = 0
4x + 3y = 26
1
Special Cases: you eliminated both variables and.....
Case 2
Case 1
# = # (and it is not a true
# = # (and it is a true
statement)
statement)
no solutions, parallel lines
infinite solutions, lines coincide
inconsistent system.
dependent system
y = 2x + 6
3y = 6x + 18
y = 1x + 7 4y = x + 8
4
2