Warm-Up 5 minutes 1) On the coordinate plane, graph two lines that will never intersect. 2) On the coordinate plane, graph two lines that intersect at.

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Warm-Up 5 minutes 1) On the coordinate plane, graph two lines that will never intersect. 2) On the coordinate plane, graph two lines that intersect at one point. 3) On the coordinate plane, graph two lines that intersect at every point (an infinite number of points).

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

Activity With your partner: Partner 1 - graph the equation 2x + 3y = 12 Partner 2 - assist partner 1 Partner 2 - graph the equation x – 4y = -5 Partner 1 - assist partner 2 How many points of intersection are there?1

Activity With your partner: Partner 1 - graph the equation x = 2y + 1 Partner 2 - assist partner 1 Partner 2 - graph the equation 3x – 6y = 9 Partner 1 - assist partner 2 How many points of intersection are there?0

Activity With your partner: Partner 1 - graph the equation 2x = 4 - y Partner 2 - assist partner 1 Partner 2 - graph the equation 6x + 3y = 12 Partner 1 - assist partner 2 How many points of intersection are there? an infinite number

Example 1 Solve the following system by graphing. x + y = 2 x = y x + y = 2 xy 2 1 -3 0 1 5 -8-6-4 -2 2 42 68 4 6 -4 -6 -8 -2 8 x = y xy 0 1 5 0 1 5 (1,1)

Practice Solve by graphing. 1)x + 4y = -6 2x – 3y = -1 2)y + 2x = 5 2y – 5x = 10

Warm-Up 4 minutes 1) y – 2x = 7 y = 2x + 8 2) 3y – 2x = 6 4x – 6y = -12 Solve by graphing.

Solving Systems of Equations by Graphing pt. 2 Check a Solution: Objectives: To determine whether an ordered pair is a solution of a system of equations

Example 1 Determine whether (3,5) is a solution of the system. y = 4x - 7x + y = 8 5 =4( ) 3 - 7 5 = 12 - 7 5 = 5 3+ 5= 8 8 = 8 (3,5) is a solution of the system

Example 2 Determine whether (-2,1) is a solution of the system. 2x – y = -53x + 2y = 3 2( )-2 - 1 = -5 -4 – 1 = -5 -5 = -5 3( ) -2 + 2( ) -6 + 2 = 3 1= 3 (-2,1) is not a solution of the system

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

Practice Solve these systems by graphing. 1)x + 4y = -6 2x – 3y = -1 2)y + 2x = 5 2y – 5x = 10

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