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

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

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

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)

( ) = -2( ) = 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 ( ) = Is (-1, -2) a solution? explain YES, because the ordered pair makes both equations true.

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

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)

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)

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)

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 = t Alligator 2:w = t Slope = w-intercept = Alligator weights WEIGHTWEIGHT time Answer? 4 months

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: evens Scales other than 1: 10,12,16?