objective l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Objective PowerPoint Presentation
Download Presentation
Objective

Loading in 2 Seconds...

play fullscreen
1 / 14

Objective - PowerPoint PPT Presentation


  • 189 Views
  • Uploaded on

Objective. The student will be able to: solve systems of equations by graphing. SOL: A.4e. 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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Objective' - Anita


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
objective
Objective

The student will be able to:

solve systems of equations by graphing.

SOL: A.4e

Designed by Skip Tyler, Varina High School

what is a system of equations
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
Intersecting Lines
  • The point where the lines intersect is your solution.
  • The solution of this graph is (1, 2)

(1,2)

parallel lines
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.
coinciding lines
Coinciding Lines
  • These lines are the same!
  • Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS!
  • Coinciding lines have the same slope and y-intercepts.
what is the solution of the system graphed below
What is the solution of the system graphed below?
  • (2, -2)
  • (-2, 2)
  • No solution
  • Infinitely many solutions
1 find the solution to the following system
1) Find the solution to the following system:

2x + y = 4

x - y = 2

Graph both equations. I will graph using x- 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
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)

2x + y = 4

x – y = 2

check your answer
Check your answer!

To check your answer, plug the point back into both equations.

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
2) Find the solution to the following system:

y = 2x – 3

-2x + y = 1

Graph both equations. Put both equations in 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 equations11
Graph the equations.

y = 2x – 3

m = 2 and b = -3

y = 2x + 1

m = 2 and b = 1

Where do the lines intersect?

No solution!

Notice that the slopes are the same with different y-intercepts. If you recognize this early, you don’t have to graph them!

check your answer12
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
What is the solution of this system?
  • (3, 1)
  • (4, 4)
  • No solution
  • Infinitely many solutions

3x – y = 8

2y = 6x -16

solving a system of equations by graphing
Solving a system of equations by graphing.

Let's summarize! There are 3 steps to solving a system using a graph.

Graph using slope and y – intercept or x- and y-intercepts. Be sure to use a ruler and graph paper!

Step 1: Graph both equations.

This is the solution! LABEL the solution!

Step 2: Do the graphs intersect?

Substitute the x and y values into both equations to verify the point is a solution to both equations.

Step 3: Check your solution.