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4-1 SOLVING
LINEAR SYSTEMS
BY GRAPHING
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
CHECKING SOLUTIONS
Example:
Is

3x
x
Is

(2, 2) a solution of the system?
2y
2y

2
6

(0, -1) a solution?
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!)
EXAMPLE
Solve

y = 2x + 5
y = -4x – 1
YOUR TURN!
Solve

y=x–1
y = -x + 3
MANY SOLUTIONS
When

will a system have infinitely
many solutions?
 When both equations are the same
line!
Example:
y = -5x – 2
5x + y = -2
NO SOLUTIONS
When

will a system have no solution?
 When the lines are parallel!
Example:
y = 3x + 1
y = 3x – 5
SUMMARY
Lines intersect
at one point.

One Solution

Both are same
line.

Infinitely Many
Solutions

Two parallel
lines.

No Solution

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4 1 solving linear systems by graphing