1. 4-1 SOLVING
LINEAR SYSTEMS
BY GRAPHING

2. WHAT IS A LINEAR SYSTEM?
A
set of two or more linear
equations.
A
solution is an ordered pair (x, y)
that makes BOTH equations true.
 Happens
graphs
at the intersection of the

3. CHECKING SOLUTIONS
Example:
Is
3x
x
Is
(2, 2) a solution of the system?
2y
2y
2
6
(0, -1) a solution?

4. SOLVING BY GRAPHING
1.
2.
3.
Graph each equation on the
same grid
Estimate the point of
intersection
Check solution in original
system (BOTH equations!)

5. EXAMPLE
Solve
y = 2x + 5
y = -4x – 1

6. YOUR TURN!
Solve
y=x–1
y = -x + 3

7. MANY SOLUTIONS
When
will a system have infinitely
many solutions?
 When both equations are the same
line!
Example:
y = -5x – 2
5x + y = -2

8. NO SOLUTIONS
When
will a system have no solution?
 When the lines are parallel!
Example:
y = 3x + 1
y = 3x – 5

9. SUMMARY
Lines intersect
at one point.
One Solution
Both are same
line.
Infinitely Many
Solutions
Two parallel
lines.
No Solution