1. 6.1 Solving systems by graphing Solving systems by graphing and analyzing special systems

2. Solution:An ordered pair that makes the equation true. Example: x + y = 7 What are some possible solutions? 5 + 2 = 7 3 + 4 = 7 -1 + 8 = 7 -10 + 17 = 7 (5,2) (3,4) (-1,8) (-10,17) The solutions are always written in ordered pairs.: How many more solutions are there?

3. System of Equations Definition: a set of two or more equations that have variables in common. Example of a system: y = 3x + 1 y = -2x - 4 Solution: ALL Any ordered pair that makes ALL the equations in a system true. Solution for this system: (-1,-2)

4. ( ) = -2( ) - 4 -2 = 2 - 4 Verify (check your answer) whether or not the given ordered pair is a solution for the following system of equations. (same system as previous slide) y = 3x + 1 y = -2x -4 ( -1,-2) ( ) = 3 ( ) + 1 -2 -2 = -3 + 1 Is (-1, -2) a solution? explain YES, because the ordered pair makes both equations true.

5. Find the solution for the following system. y = 3x + 1 y = -2x - 4 m= 3; b = 1 m= -2; b = -4 Solution: (-1, -2)

6. Find the solution for the following system. 2x + y = 3y = -2x + 3 y = 3x - 2 m= -2; b = 3 m= 3; b = -2 Solution: (1, 1)

7. Find the solution for the following system. y = ½ x + 1 2y – x = 2 m= ½; b = 1 x –int= y –int= -2 1 Solution: Infinitely many solutions (because the lines are the same)

8. Find the solution for the following system. y = 2x + 2 y = 2x - 1 m= 2; b = 2 m= 2; b = -1 Solution: No solution (because the lines are parallel)

9. Writing a system of equations. Scientists studied the weights of two alligators over a period of 12 months. The initial weight and growth rate of each alligator are shown below. After how many months did the alligators weigh the same amount? Alligator 1 Initial weight: 4 pounds Rate of growth: 1.5 lb/ month Alligator 2 Initial weight: 6 pounds Rate of growth: 1 lb/ month Alligator weight (w) = ___________ + ________________________ Initial weight Growth ratetimes Time (t) Alligator 1:w = 4 + 1.5t Alligator 2:w = 6 + 1 t Slope = w-intercept = 1.5 1 4 6 Alligator weights 12 10 8 6 4 2 0 WEIGHTWEIGHT 0 1 2 3 4 5 6 time Answer? 4 months

10. Systems with infinitely many solutions or no solutions. Slopes: different Intersect: one point Slopes: same y-intercept: same The lines are the same Slopes: same Lines are parallel lines don’t intersect Assignment: pg 367: 10-38 evens Scales other than 1: 10,12,16?