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 transcript:

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

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

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

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.

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

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.

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)

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

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

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

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

Homework Page 339 #27, 28, 30, 32