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Systems of Equations By Graphing What is it? • A system compares to functions and determines when they intersect (where they have the same x and y values). Point of intersection 3 methods of solving • Graphing • Substitution • Elimination *Graphing is an estimate. The other two methods are exact. Steps 1. 2. 3. 4. Solve for y in each equation. Graph them both on the same axes. Identify the point where they cross. That point (x,y) is the “solution” to the system. Example = 4 − 1 + =4 You try 1 = +4 3 1 =− +2 3 You try again 12 − 9 = 27 8 − 6 = 18 Sometimes you will have to write the equation… The new Six Flags is offering 2 payment plans. Option 1: $5 entrance fee and $1 per ride. Option 2: $2 entrance fee and $3 per ride. Which option would you choose? What factors should you consider? Option 1: $5 entrance fee and $1 per ride. Option 2: $2 entrance fee and $3 per ride. Y=cost X=# of rides = 1 + 5 = 3 + 2 Solution: (1.5 , 7) If you ride more than 2 rides, option 1 is better. You try with a partner! Find the value of two numbers if their sum is 12 and their difference is 4. 4 and 8 • The difference of two numbers is 3. Their sum is 13. Find the numbers. 5 and 8 This is a thinker…. • A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. What is the speed of the boat in still water? What is the speed of the current? Solution • Let y = boat speed in still water Let x = speed of the current then (y-x) = effective speed upstream (y+x) = effective speed downstream • 12(y+x) = 336 • 14(y-x) = 336 • y - x = 24 y + x = 28 Graph • boat: 26 mph, current: 2 mph Homework