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Solving Systems of Equations by

Graphing

I can:

Solve systems of equations by graphing

Determine whether a system of equations is consistent and independent, consistent and dependent, or inconsistent.

Systems of equations…recall that… x + y = 9 x – y = 5 x = 2, y = 7 or (2, 7)

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Two equations together make a system the solution of the system is the point of intersection.

There are lots of ways to solve system of equations.

Today, you will solve systems of equations by GRAPHING.

EXAMPLE #1

Solve the system by graphing y = 2x + 3 y = -

½ x + 3

First, graph y = 2x + 3

Then, graph y = -

½ x + 3

Find the coordinates of the point where the lines cross

Solution: x = 0, y = 3

**(0, 3)**

Consistent and Independent?

Consistent and Dependent?

Inconsistent?

EXAMPLE #2

Solve the system by graphing

3x

– 3y = 9 y = -x + 1

Notice the first equation is not in y = mx + b form.

3x

– 3y = 9

-3x -3x

– 3y = -3x + 9

-3 -3 -3 y = 1x + -3

EXAMPLE #2

Continued…..

y = 1x + -3 y = -x + 1

First, graph y = 1x + -3

Then, graph y = -1x + 1

Find the coordinates of the point where the lines cross

Solution: x = 2, y = -1

**(2, -1)**

Consistent and Independent?

Consistent and Dependent?

Inconsistent?

**Solve the system of equations by graphing.**

**Answer:**

(4

,

1)

Consistent and Independent?

Consistent and Dependent?

Inconsistent?

1.

Make sure each equation is in y = mx + b form.

2.

3.

4.

Enter equations in

**y = **

menu

Hit **ZOOM **then **“6” **for standard window

To find the intersection of your equations, hit:

**2 nd**

**“TRACE”**

**#5 – “INTERSECT”**

**ENTER**

EXAMPLE #3

Solve the system by graphing y = 2x + 3 y = 2 x

– 5

First, graph y = 2x + 3

Then, graph y = 2x

– 5

**Parallel!**

Find the coordinates of the point where the lines cross

No solution (lines don’t intersect)

Consistent and Independent?

Consistent and Dependent?

Inconsistent?

EXAMPLE #4

Solve the system by graphing y = -2x + 7

4x + 2y = 14

Notice the second equation is not in y = mx + b form.

4x + 2y = 14

-4x -4x

2y = -4x + 14

2 2 2 y = -2x + 7

Wait! This is the same as the first equation!

EXAMPLE #4

Continued…..

y = -2x + 7 y = -2x + 7

First, graph y = -2x + 7

Then, graph y = -2x + 7

Find the coordinates of the point where the lines cross

Infinitely many solutions

**They overlap!**

Consistent and Independent?

Consistent and Dependent?

Inconsistent?

**Graph the system of equations and describe it as consistent and **

*independent*, *consistent and dependent*, or *inconsistent*.

Since the equations are equivalent, their graphs are the same line.

**Answer:**

Consistent and Independent?

Consistent and Dependent?

Inconsistent?

Describe the differences between…

Consistent and Independent:

Consistent and Dependent:

Inconsistent:

Skills Practice Worksheet

#’s 1 – 6, 10 -12