This document discusses systems of linear equations and inequalities, including: defining a system as a collection of equations dealt with together; solutions being ordered pairs that satisfy all equations; examples of determining if points are solutions; solutions being intersections of lines; determining the number of solutions based on whether lines intersect, are the same, or are parallel.

1. Systems of Linear Equations
and Inequalities

3.  A set or collection of equations that
you deal with all together at once.
 A solution of a two variable system is
an ordered pair (x, y) that makes
BOTH equations true.

4.  Example:
 Is (2, 2) a solution of system?
3x 2 y 2
x 2y 6
 Is (0, -1) a solution?

5.  Solution of one equation: any point on
the line.
 Solution of a system: point that falls on
BOTH lines.
 Example:
y 3x 2
y x 6

6.  Graph the system and find the solution.
2x 2 y 8
2x 2 y 4

7.  When will a system have infinitely many
solutions?
◦ When both equations are the same line!
Example:
3x 2 y 6
6 x 4 y 12

8.  When will a system have no solution?
◦ When the lines are parallel!
Example:
3x 2 y 6
3x 2 y 2

9.  Tell how many solutions each linear
system has.
 1. 2 x 4 y 12
x 2y 6
 2. x y 5
2x 2 y 9

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