Unit 6 – Systems of Equations

Topic: Solving Systems of Linear Equations by Graphing

What is a system of equations?Set of equations with two or more variables.

Example: x + 2y = 6 x – y = 3

Solution to a system of linear equations is an ordered pair that makes each equation true.Example: (4, 1) is the solution to the above

system, because it makes each equation true. 4 + 2(1) = 6 4 – 1 = 3

Types of systems (Put on a note card)Independent system

System with exactly one solution.Graph of system contains two intersecting

lines (equations have different slopes).Dependent system

System with infinitely many solutions.Graph of system contains coinciding lines

(both equations have same slope & y-intercept).

Inconsistent systemSystem with no solutions.Graph of system contains parallel lines

(same slope, different y-intercepts).

Solving Linear Systems: GraphingGraph each equation.

The point where the two lines intersect is the solution to the system.

You should ALWAYS check your solution algebraically by substituting the solution point for x & y in each equation.

Graph each line and find the intersection.

The lines appear to intersect at (2, 1). Check solution algebraically by substituting (2, 1) into each equation.

32

221

xy

xy{Solving Linear Systems: Graphing

11

211

2)2(1

2

?

21

?

21

y

11

341

3)2(21

32

?

?

xy

Both statements are true; (2, 1) is the solution to this system.

32

221

xy

xy{Solving Linear Systems: Graphing

This second equation is ugly! Let’s rewrite in slope-intercept form.

Move y to the left and x to the right.

64

14

yx

xy{Solving Linear Systems: Graphing

4 4

64

xyxy

yx

Both lines have the same slope, so they are parallel. This is an inconsistent system with no solution (so there’s no reason for us to actually graph it).

64 xy

JOURNAL ENTRYTITLE: Solving Systems Graphically 3-2-1Review your notes from this presentation and

identify 3 things you already knew, 2 things you learned, and one question you still have.

HomeworkTextbook Section 6-1 (pg. 386): 2-16Due 1/17 (B-day) or 1/18 (A-day)