Transcript 6-1 Solving systems by graphing

WARM UP
Find roads that intersect once, more than once, and never
intersect. Describe the roads as intersecting lines, curves,
or parallel lines.
THINK & DISCUSS
How can you show all the solutions of the linear equation y = 2x – 3?
Two or more linear equations together form a system of linear
equations. One way to solve a system of linear equations is by
graphing. Any point common to all the lines is a solution of the
system.
SOLVE THE SYSTEM OF LINEAR EQUATIONS BY GRAPHING
y = 2x – 3
y=x–1
Check
your
answer!
SOLVE THE SYSTEM OF LINEAR EQUATIONS BY GRAPHING
y=x+5
y = -4x
Check
your
answer!
SOLVING SPECIAL TYPES OF SYSTEMS
A system of linear equations has
no solution when the graphs of the
equations are parallel. There are no
points of intersection, so there is no
solution.
A system of linear equations has
infinitely many solutions when the
graphs of the equations are the
same line. All points on the line are
solutions of the system
SOLVE BY GRAPHING
4y4y== 44 ++xx
1
x
4
1 + y = -1
x + y = -1
4
SOLVE BY GRAPHING
y=x
y=x+6
SOLVE BY GRAPHING
2x ++2y2y
= 1= 1
2x
y = -x +
1
2
1
y = -x +
2
SOLVE BY GRAPHING
x=1
x = -2
ENTERTAINMENT
A cable company offers a “pay-per-view” club. Let
c = the annual cost and n = the number of movies
you watch in a year. Write a system of linear
equations to decide whether to join the club.
HOMEWORK
Pg 272 # 1 – 10