Solve Systems By Graphing

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Systems of Equations

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

Slide 2  Intersecting Lines
 The point where the lines intersect is your solution.
 The solution of this graph is (1, 2)
 (1,2)

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 yintercepts.

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 yintercepts.

Slide 5  What is the solution of the system graphed below?
 (2, 2)
 (2, 2)
 No solution
 Infinitely many solutions

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 yintercepts (plug in zeros).
 Graph the ordered pairs.
 2x + y = 4
 (0, 4) and (2, 0)
 x – y = 2
 (0, 2) and (2, 0)

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

Slide 8  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!

Slide 9  2) Find the solution to the following system:
 y = 2x – 3
 2x + y = 1
 Graph both equations. Put both equations in slopeintercept or standard form. I’ll do slopeintercept form on this one!
 y = 2x – 3
 y = 2x + 1
 Graph using slope and yintercept

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 yintercepts. If you recognize this early, you don’t have to graph them!

Slide 12  Check your answer!
 Not a lot to check…Just make sure you set up your equations correctly.
 I doublechecked it and I did it right…

Slide 13  What is the solution of this system?
 3x – y = 8
 2y = 6x 16
 (3, 1)
 (4, 4)
 No solution
 Infinitely many solutions

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 yintercepts. 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.