3-1 Solving Linear Systems by Graphing (Day 1)

Objective CA 2.6 Students solve systems of

linear equations and inequalities (in two or

three variables) by substitution, graphs, or

matrices.

A system of two linear equations in two variables

x and y consists of two equations of the

following form Ax By C Dx Ey F

If two lines intersect, how many points do both

lines have in common?

One

The point of intersection (x, y) must be a valid

solution to both line equations.

Example 1 Checking Solutions of a Linear

System Check whether the following are solutions

to the system a) (2, 2) b) (0, -1)

Solution a)

Since (2, 2) is a solution of each equation, it

is a solution of the system of equation.

Solution b)

Since (0, -1) is not a solution of equation 2, it

is not a solution of the system.

Solving a System of equations by Graphing

Step 1 Get in slope-intercept form

Step 2 Graph each equation

Step 3 Identify where graphs

intersect

Example 2 Solving a system graphically. Solve

the system.

Step 1) Begin by graphing both

equations.

Equation 1

Equation 2

From the graph, the lines appear to intersect at

(2, 1).

From the graph, the lines appear to intersect at

(2, 1). Check this algebraically by substitution

into the original equations.

The solution is (2, 1).

Systems of Equations may have infinite number of

solutions. If the two equations are equivalent

they represent the same line.

Example 3 Tell how many solutions the linear

system has. a)

Graph the equations.

These equations represent the same line.

If the two equations are of the same line they

will have the same equation when converted to the

slope intercept form of the linear equation.

Tell how many solutions the linear system has.

Graph the two equations.

If two lines are parallel they have the same

slope but different y-intercepts.

Homework Page 143 12 46 even, 53 - 55 all

A system of equations may have no solutions in

common. If two lines never intersect, then they

are parallel.