Objective

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# Objective - PowerPoint PPT Presentation

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.

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## Objective

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Presentation Transcript
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.
• 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 graph is (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.
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?
• (2, -2)
• (-2, 2)
• No solution
• Infinitely many solutions
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.

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

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 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 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!

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?
• (3, 1)
• (4, 4)
• No solution
• Infinitely many solutions

3x – y = 8

2y = 6x -16

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.