February 05, 2013
Chapter 7:
Systems of Equations and Inequalities
7.1 Solving Systems by Graphing
Objectives
• Be able to solve systems of equations by graphing
• Be able to analyze special types of systems
February 05, 2013
System of linear equations: Two or more linear equations together
y = 2x ­ 3
y = x ­1
Solution to a system of equations: • The point (x, y) where the lines intersect. • Any point that makes all of the equations true
y = 2x ­ 3
y = x ­1
The solution to this system is (2,1)
February 05, 2013
A solution to a system of equations is the point (x, y) where the lines cross
y = ­2x + 1
y = ­2x ­ 1
There is no solution because the lines are parallel!
Critical Thinking: How can you tell if a system has no solution before you graph it?
A solution to a system of equations is the point (x, y) where the lines cross
2x + 4y = 8
y = ­1/2x + 2
There are infinitely many solutions because the lines are the same!
February 05, 2013
One Solution
No Solution
Infinitely many
solutions
Solve the system
y = x + 2
y = ­2x + 2
February 05, 2013
Solve the system
y = ­2x + 1
y = ­2x ­ 4
Solve the system
y + x = 4
2x + 2y = 8
February 05, 2013
Homework #11:
Graphing Systems WS
#10 ­ 18