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6-1 Linear Systems Goal: Solve a system of linear equations by graphing Eligible Content: A1.1.2.2.1 / A1.1.2.2.2.

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Presentation on theme: "6-1 Linear Systems Goal: Solve a system of linear equations by graphing Eligible Content: A1.1.2.2.1 / A1.1.2.2.2."— Presentation transcript:

1 6-1 Linear Systems Goal: Solve a system of linear equations by graphing Eligible Content: A / A

2 Vocabulary System of Linear Equations – two or more linear equations using the same variables. EXAMPLE: 2x + 3y = 12 4x – 2y = 8

3 Vocabulary Graphing Method – a method for solving linear systems that involves graphing two lines to find the point of intersection.

4 Vocabulary Solution any ordered pair that works in both equations.
the point on the graph that the two lines cross. Point of Intersection – the point the two lines cross. It is the solution to the system.

5 Checking Solutions Is the point (2, -1) a solution to the system: 3x + 2y = 4 -x + 3y = -5 YES Is the point (4, 3) a solution to the system: 2x + 3y = 17 -4x + 3y = -10 NO

6 To Find Solutions by Graphing
Write each equation in y = mx + b form Graph both equations in the same coordinate plane. Estimate the point of intersection. Check your solution.

7 Solve the system by graphing: y = 3x + 4 2x + y = 9 m = 3 b = 4 -2x -2x y = -2x + 9 m = -2 b = 9
(1, 7) The solution is (1,7)

8 Examples y = 2x – 1 y = x + 1 y = -2x + 3 y = x – 3 x + y = -2
(2, 3) (2, -1) (-3, 1)

9 Examples 3x + 2y = 4 -x + 2y = -4 5x + y = 8 2x – 2y = -4
(2, -1) (1, 3)

10 Graph the system of equations and determine the solution.
B. (3, 0) C. (2, 3) D. (3, 3)

11 Practice y = ½ x + 2 y = -x + 5 2x + y = 6 -2x + y = -10 3x + y = 11
(2,3) (4, -2) (4, -1)

12 Homework Page 339 #27, 28, 30, 32


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