This document discusses solving linear systems of equations by graphing. A linear system is a set of two or more linear equations where a solution is an ordered pair that satisfies both equations. Graphing the equations on the same grid allows you to find the point of intersection, which is the solution. Systems can have one solution, infinitely many solutions if the lines are the same, or no solution if the lines are parallel.

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