# Solve Systems By Graphing

Systems of Equations

# Solve Systems By Graphing

Created 3 years ago

Duration 0:08:04
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Slide Content
1. ### Slide 1 - Objective

• The student will be able to:
• solve systems of equations by graphing.
• SOL: A.4e
• Designed by Skip Tyler, Varina High School
• Modified by Mr. Burns
2. ### Slide 2 - Intersecting Lines

• The point where the lines intersect is your solution.
• The solution of this graph is (1, 2)
• (1,2)
3. ### Slide 3 - 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.
4. ### Slide 4 - 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.
5. ### Slide 5 - What is the solution of the system graphed below?

• (2, -2)
• (-2, 2)
• No solution
• Infinitely many solutions
6. ### Slide 6 - 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)
7. ### Slide 7 - 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

• 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!
9. ### Slide 9 - 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
10. ### Slide 11 - 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…
12. ### Slide 13 - What is the solution of this system?

• 3x – y = 8
• 2y = 6x -16
• (3, 1)
• (4, 4)
• No solution
• Infinitely many solutions
13. ### Slide 14

• 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 use a 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.