5.1 Solving Systems of Equations by Graphing

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Presentation transcript:

5.1 Solving Systems of Equations by Graphing Objectives: To find the solution of a system of equations by graphing

Warmup

A System of linear equations is a set of two or more linear equations Example: y = 2x + 5 and 3x +2y =12 A solution of a system of equations is an ordered pair that is a solution to each equation (x,y)

Example 1 Solve the following system by graphing. x + y = 2 x = y x y 2 -8 -6 -4 -2 2 4 6 8 1 1 5 -3 (1,1) x = y x y 1 1 5 5

Practice Solve by graphing. x + 4y = -6 2x – 3y = -1 y + 2x = 5

Example 2 Determine whether (3,5) is a solution of the system. y = 4x - 7 x + y = 8 5 = 4( ) 3 - 7 3 + 5 = 8 5 = 12 - 7 8 = 8 5 = 5 (3,5) is a solution of the system

Example 3 Determine whether (-2,1) is a solution of the system. 2x – y = -5 3x + 2y = 3 2( ) -2 - 1 = -5 3( ) -2 + 2( ) 1 = 3 -4 – 1 = -5 -6 + 2 = 3 -5 = -5 (-2,1) is not a solution of the system

Practice Determine whether the given ordered pair is a solution of the system. (2,-3); x = 2y + 8 2x + y = 1 (-3,4); 2x = -y – 2 y = -4

Practice Solve these system by graphing. Y + 2x = 5 2y – 5x =10