3.2b ­ Solve by Substitution (Special Cases) Notes
Bell Ringer
When solving a system of linear equations using substitution, how would
you determine which variable (x or y) to solve for when determining
the substitution expression?
Finished with bell work? Check your homework: Pg. 194 #2­5 and Pg 213 #7­9
Must show all work to get credit for answer. Turn homework into basket.
Pg 194
Pg 213
2. (5,12)
7. (2,5)
3. (8,­11)
8. (5,3)
4. (­7,­16)
9. (4,­1)
5. (­2,­1)
Solving Linear Systems: Special Cases
Case 1
Exactly One Solution
Lines have different slopes
Case 2
Infinitely Many Solutions
Lines have same slope.
& same y­intercept.
Special Case
Case 3
No Solution
Lines have same slope.
& different y­intercept.
Special Case
3.2b ­ Solve by Substitution (Special Cases) Notes
Infinitely Many Solutions
Solve by using the Substitution Method.
EX 1: EX 2: No Solution
Solve by using the Substitution Method.
EX 1: EX 2: 3.2b ­ Solve by Substitution (Special Cases) Notes
Homework: Pg. 194 #10­13 determine type of solution ­ No Solution or Infinitely Many
Pge. 213 #1­3 (Solve by Substitution not by graphing)