Solve Systems by Graphing PowerPoint Notes

8/9/2019 Solve Systems by Graphing PowerPoint Notes

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Objective

The student will be able to:

solve systems of equations by graphing.

SOL: A.9

Designed by Skip Tyler, Varina High School



What is a system of equations?

A system of equations is when you have

two or more equations using the same

variables. The solution to the system is the point

that satisfies ALL of the equations. This

point will be an ordered pair.

When graphing, you will encounter three

possibilities.



Intersecting Lines

The point where the lines

intersect is your solution.

The solution of this graphis (1, 2)

(1,2)



Parallel Lines

These lines never

intersect!

Since the lines never

cross, there is

NO SOLUTION!

Parallel lines have the

same slope with different

y-intercepts.

2Slope = = 2

1

y-intercept = 2

y-intercept = -1



Coinciding Lines

These lines are the same!

Since the lines are on top

of each other, there are

INFINITELY MAN Y

SOLUTIONS!

Coinciding lines have the

same slope and

y-intercepts.

2lope 2

1

y-intercept -1



What is the solution of the system

graphed below?

1. (2, -2)

2. (-2, 2)

3. No solution

4. Infinitely many solutions



1) Find the solution to the following

system:

2x + y = 4

x - y = 2

Graph both equations. I will graph usingx- and y-intercepts (plug in zeros).

Graph the ordered pairs.

2x + y = 4

(0, 4) and (2, 0)

x ± y = 2

(0, -2) and (2, 0)



Graph the equations.

2x + y = 4

(0, 4) and (2, 0)

x - y = 2

(0, -2) and (2, 0)

Where do the lines intersect?

(2, 0)



Check your answer!

To check your answer, plugthe point back into bothequations.

2x + y = 4

2(2) + (0) = 4

x - y = 2(2) ± (0) = 2 Nice job«let¶s try another!



2) Find the solution to the following

system:

y = 2x ± 3

-2x + y = 1

Graph both equations. Put both equationsin slope-intercept or standard form. I¶ll do

slope-intercept form on this one!

y = 2x ± 3

y = 2x + 1

Graph using slope and y-intercept



Graph the equations.

y = 2x ± 3

m = 2 and b = -3

y = 2x + 1m = 2 and b = 1

Where do the lines intersect?No solution!

Notice that the slopes are the same with differenty-intercepts. If you recognize this early, you don¶t

have to graph them!



Check your answer!

Not a lot to check«Just

make sure you set up

your equations correctly.I double-checked it and I

did it right«



What is the solution of this system?

3x ± y = 8

2y = 6x -16

1. (3, 1)

2. (4, 4)

3. No solution4. Infinitely many solutions



Solving a system of equations by graphing.

Let's summarize! There are 3 steps to

solving a system using a graph.

Step 1: Graph both equations.

Step 2: Do the graphs intersect?

Step 3: Check your solution.

Graph using slope and y ± intercept

or x- and y-intercepts. Be sure to usea ruler and graph paper!

This is the solution! LABEL the

solution!

Substitute the x and y values into

both equations to verify the point is a

solution to both equations.

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