6-1 solving systems by graphing

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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

4y = 4 + x

x + y = -1

SOLVE BY GRAPHING

y = x

y = x + 6

SOLVE BY GRAPHING

2x + 2y = 1

y = -x +

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