UNIT 1 LINEAR MPM 2 D SYSTEMS 1

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UNIT 1: LINEAR MPM 2 D SYSTEMS

UNIT 1: LINEAR MPM 2 D SYSTEMS

1. LINEAR SYSTEM v. System of equations: a set of two or more equations

1. LINEAR SYSTEM v. System of equations: a set of two or more equations with two or more variables v. A system of linear equations may intersect at one or more points §These points of intersection (P. O. I) are called the solutions to the system of equations

TASK 1 v. Graph the following lines: (1)y=2 x+4 (2)y=2 x v. How many

TASK 1 v. Graph the following lines: (1)y=2 x+4 (2)y=2 x v. How many points of intersection do they have?

TASK 1 v. No P. O. I

TASK 1 v. No P. O. I

TASK 2 v. Graph the following lines: (1)y=2 x+4 (2)y=-x+4 v. How many points

TASK 2 v. Graph the following lines: (1)y=2 x+4 (2)y=-x+4 v. How many points of intersection do they have?

TASK 2 v. One P. O. I

TASK 2 v. One P. O. I

TASK 3 v. Graph the following lines: (1)y=x-3 (2)4 x-4 y=12 v. What do

TASK 3 v. Graph the following lines: (1)y=x-3 (2)4 x-4 y=12 v. What do you notice?

TASK 3 v. Infinite P. O. I v. Every point is a P. O.

TASK 3 v. Infinite P. O. I v. Every point is a P. O. I

SCHEDULE 1. Attendance 2. Finish Lesson on Linear Systems A. Practice 3. 1. 8:

SCHEDULE 1. Attendance 2. Finish Lesson on Linear Systems A. Practice 3. 1. 8: Substitution A. Practice

SUMMARY v. For NO SOLUTION: §Same slope and different y-intercepts v. For exactly ONE

SUMMARY v. For NO SOLUTION: §Same slope and different y-intercepts v. For exactly ONE SOLUTION §Different slopes only v. For INFINITELY MANY SOLUTIONS §Same slope and same y-intercept

LEARNING CHECK 1. Will two lines with slopes that are the negative reciprocal of

LEARNING CHECK 1. Will two lines with slopes that are the negative reciprocal of one another ever intersect? a) YES! They will be perpendicular to one another

2. SOLVING LINEAR SYSTEMS ALGEBRAICALLY v. Ex. 1: Determine the number of solutions to

2. SOLVING LINEAR SYSTEMS ALGEBRAICALLY v. Ex. 1: Determine the number of solutions to this system (algebraically) (1)2 x+3 y=10 (2)10 x+15 y=50 Put both equations into y=mx+b form and compare their slopes and y-intercepts

2. SOLVING LINEAR SYSTEMS ALGEBRAICALLY v. Ex. 1: Determine the number of solutions to

2. SOLVING LINEAR SYSTEMS ALGEBRAICALLY v. Ex. 1: Determine the number of solutions to this system (algebraically)

ASSIGNED WORK P. 69 #1, 3, 5, 7, 8, 13 ac Reminders: -Keeping an

ASSIGNED WORK P. 69 #1, 3, 5, 7, 8, 13 ac Reminders: -Keeping an organized and complete binder/portfolio is a part of your final grade