This document discusses solving systems of linear equations graphically and algebraically. It explains that a system will have one solution if the lines intersect at one point, infinitely many solutions if the lines are the same or parallel, and no solution if the lines do not intersect. Algebraically, a system has infinitely many solutions if the equations are always true and no solutions if they are never true. Two examples of solving systems algebraically are shown.

1. 4-4 SPECIAL
LINEAR SYSTEMS

2. WHEN GRAPHING:
Remember:
Lines intersect
at one point.
One Solution
Both are same
line.
Infinitely Many
Solutions
Two parallel
lines.
No Solution

3. SOLVING ALGEBRAICALLY
If
you end up with something
that is ALWAYS true:
System has infinitely many
solutions.
 Examples:
0
=0
2 = 2
 -7 = -7
 etc…

4. If
you end up with something
that is NEVER true:
System has no solutions.
 Examples:
 -5
=1
0 = 3
 -2 = 2
 etc…

5. EXAMPLE
Solve:
4x + 8y = 36
12x + 24y = 108

6. EXAMPLE
Solve:
y = 3x + 1
-3x + y = -5

7. YOU TRY!
Solve:
2x + y = 5
4x + 2y = 0