Bellwork 1.) How many different ways can 2 lines appear on a graph? 2.) What are they? 3.) How many solutions are there for each of the different ways 2 lines can appear on a graph?

Objective To be able to determine the number of solutions of a system of equations by either solving by graphing or substitution.

Graph y = x + 3 & 2y = 2x + 6 2y = 2x + 6 y = x + 3 Solution= infinite

Solve by Substitution y = x + 3 2y = 2x + 6 So….. 2(x + 3) = 2x + 6 (Distribute 2) 2x + 6 = 2x + 6 (Subtract 2x) 6 = 6 Solution = infinite

Graph y = 3x + 1 & 4y -12x = 8 4y - 12x = 12 y = 3x + 1 Solution= none

Solve by Substitution y = 3x + 1 4y - 12x = 8 So…... 4(3x + 1) - 12x = 8(Distribute 4) 12x + 4 - 12x = 8 (C L T) 4 = 8 Solution = none

Identifying the solutions There are 3 ways 2 lines can appear on a graph. 1.) They cross at 1 point 2.) They are Parallel 3.) They are the same line

Identifying the solutions 1.) They cross at 1 point (2, -4) One 2.) They are Parallel 4 = 8 None 3.) They are the same line 6 = 6 Infinite

Identify the # of solutions 1.) 7=7 2.) (2,3) 3.) 4=-4 4.) 0=0 1.) Infinite 2.) One 3.) None 4.) Infinite

Identify the # of solutions 5.) 0=5 6.) 2=3 7.) (4,-4) 8.) 6=6 5.) None 6.) None 7.) One 8.) Infinite

Graph and find the # of Solutions 1.)x - y = 3 x - y = -2 1.)y = x -3 y = x + 2

Graph y = x -3 y = x + 2 Y X Solution= none

Classwork Do Worksheet 7-5 Homework Page 377 (1-15 )