1. 3.1 and 3.2 Systems of Equations, Day #1 tmeyer2@eden.rutgers.edu http://honorsalgebra2meyer.wikispaces.com

2. Do Now! (Please) With the help of your graphing calculator and a partner, solve this problem. (Use 0-10 on the x-axis and 0-5 on the y-axis) The coolest person ever is trying to decide between long distance phone carriers. They offer the following prices: Find equations to model the cost “y” of each plan for “x” minutes and graph your equations on the calculator. Under which circumstances is each plan most desirable? EXPLAIN. PlanCost for First Minute Cost for each Additional Minute Phrequent Phoner$0.20$0.17 Pals and Buddies$0.50$0.11

3. Homework Concerns? Are there any?

4. That’s Schrodinger’s Cat!

5. Do Now Solution Phrequent Phoner: y=.20+.17(x-1)=.20+.17x-.17=.17x+.03 Pals and Buddies y=.50+.11(x-1)=.50+.11x-.11=.11x+.39 1) Hit “WINDOW”2) Hit “Y=“ X min=0Y1=.17x+.03 X max=10Y2=.11x+.39 X scl=1 Y min=03) Hit “GRAPH” Y max=54) Hit “2 nd -TRACE” (Calc) Y scl=15) Hit “5: intersect” X res=16) Hit “ENTER” 3 times

6. The intersection point is….. (6, 1.05) What does this mean? 7) If you wish to hit “TRACE”, you can move along the two lines. Hit up or down to switch lines. 8) Now….hit “2 nd -Graph” and you will see a table. Comment. So…..which plan is better when? For less than 6 minutes, the Phrequent Phoner is cheaper. For more than 6 minutes, Pals and Buddies is cheaper.

7. Brought to You by the College Board….. 1) If, what is ? Just substitute 6 where you see 4x+y. The result is (6-3) 2 =9. 2) If 4x+3y=14 and 3x-3y=13, what is 7x? 4x+3y=14 3x-3y=13 Use linear combinations! 7x=27 Other ways?

8. Systems Graph each system, then determine whether the system has one solution (name it!), no solution, or infinitely many solutions. Test your answers using algebra! 1) 2) 3)

10. Two algebraic methods exist for solving this: a)The Substitution Method 1) Take the first equation and solve for any variable, say y. y=3-x Now plug this in where you see y in the second equation. 3x-y=3x-(3-x)=3x-3+x=4x-3=1 So x=1. Plug this in to either equation (check with both!) to find y. 1+y=3, so y=2. The solution is the point (1,2).

11. Two algebraic methods exist for solving this: b)The Linear Combination Method We combine the equations. Multiply one or both of the equations by a constant first if necessary. Here we see that if we add these equations, the ys will cancel out. So x+y=3 +3x-y=1 4x=4 x=1 Plug into either equation to get y (check both!) x+y=1+y=3, so y=2. Again, (1,2) is the solution.

13. We can use either method. Since we have y=STUFF, I will use substitution. So plug the bottom equation into the top. 2x+y= 2x+(-2x+1)=1 But 2x+y=-3. Surely 1 and -3 aren’t the same number NO SOLUTIONS Why not?

15. You can use either method to solve this algebraically. I will use Linear Combination for demonstrative purposes. Write both equations in standard form. x+y=-3 -2x-2y=6 Let’s multiply the top by 2 before combining so that something will cancel. 2(x+y)=2(-3) (2*equation #1) 2x+2y=-6 (Simplified) +-2x-2y=6 (Equation #2) 0+0=0 0=0 Of course! Infinitely many solutions! Why?

16. Word Problems! A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test? Let x=the number T/F questions and y=the number of MC questions So Answer: 5 Multiple Choice Questions

17. More Challenging! The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number. Hint: Let t=the tens digit and u=the units digit Remember: 26=10*2+1*6 Equation 1 is simple to get: t+u=7 Equation 2: Original Number: 10t+1u (Why? 26=10*2+1*6) Reverse the digits: 10u+1t It is now equal to the original number increased by 27. So 10u+1t=10t+1u+27

18. Cont. We get t=2 and y=5 so that the number is 25.