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System of 1 st Degree Equations with 2 Variables

System of 1 st Degree Equations with 2 Variables. Solving a system of equations (2 rules) to find the ordered pair ( x,y ) that is common to both rules. Example: To rent a car you are given 2 choices. Choice A Choice B

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System of 1 st Degree Equations with 2 Variables

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  1. System of 1st Degree Equations with 2 Variables

  2. Solving a system of equations (2 rules) to find the ordered pair (x,y) that is common to both rules • Example: To rent a car you are given 2 choices. Choice AChoice B Costs 0.30¢ per km. Cost is $30 and then 0.20¢ per km. Write the rules for each situation Choice A y = 0.30x Choice B y = 0.20x + 30

  3. Question: How many km will you drive for the cost to be the same? Create 1 Table of Values for both situations If you drive 300 km, the cost will be the same for choices A and B

  4. Graph this situation cost Point of intersection of the 2 lines is called the SOLUTION SET • (300,90) x , y The point of intersection must match your table of values !! 10 50 # of km

  5. What and where is the solution set? • What???? • It is the point where the value of x has the same value of y in both situations. • Where???? • It is found in the table of values. Look for the x that has the same y value below it. • It is found on the graph. Look to see where the two lines intersect.

  6. You have been given the choice of two options for a babysitting job. Example #2 Option #1 You will be paid $4 an hour. Option #2 You will be paid $5 initially and then $3 an hour. After how many hours will it not matter which payment option you choose? 1- write the rules(system of equations) 2- make table of values 3- draw the graph 4- answer the question

  7. Write out the rules for the two options Option #1 y = 4x Option #2 y = 5 + 3x Table of Values Looking at the table of values, the solution set is found at (5, 20). This means that after working 5 hours, you would make $20 regardless of which option you choose.

  8. Graphing to find solutions set • Pay Solution set (5,20) 2 1 # hours

  9. Workbook page 122 Activity #1 4306then do page 124question #1 a,c,dthey give you the rules…you make the table of values and the graph.

  10. Page 124 #1 a

  11. Comparison Method Using the algebraic method is much easier and faster than table of values and graphing. We want to know when the y is the same…so we make the equations equal to each other Y = 0.30x Y = 0.20x + 30 0.30x = 0.20x + 30 0.30x – 0.20x = 0.20x + 30 – 0.20x 0.10x = 30 0.10 0.10 X = 300

  12. Now that you have the x, how do you find the y ??? To find the “y” substitute the answer you got for x into EITHER of the rules…pick the easier one ! Now you have both answers for the solution set….. (300,90) Y= 0.30x Y = 0.30 • 300 Y= 90

  13. Example #2: Your family needs to choose between two vacations. Miami Costs $25oo for airfare Costs $170 per night New Orleans $2950 airfare $140 per night Question #1 : How many nights would you stay for the cost to be the same? Question #2 : What would the cost be?

  14. Write the system of equations to begin: Ym = 2500 + 170x Yn = 2950 + 140x 2500 + 170x = 2950 + 140x 2500 + 170x -140x = 2950 +140x -140x 2500 + 30x = 2950 2500 + 30x – 2500 = 2950 -2500 30x = 450 30 X = 15 Y = 2500 + 170(15) Y= 2500 + 2550 Y = 5050 Answers: Question 1 = 15 days Question 2 = $5050

  15. If you want to go for more than 15 nights…which city would be the less expensive? Miami for 20 nights Y = 2500 + 170(20) y-= 2500 + 3400 Y= 5900 New Orleans Y=2950 + 140(20) Y= 2950 + 2800 Y=5750

  16. Math 4306 For next Tuesday morning you MUST have the following finished: Page 124 #1 a,b,c,d (use comparison notes) #2 Page 125 #3,4 Page 127 #7 Be quiet and begin NOW you have 25 minutes to work on this. ‘translate this …” means write the 2 rules !

  17. Workbook 396-92page 124 #1 a,b,c,d find solutions set by comparison #2 allPage 125 allpage 126 allpage 127 allfinish for tomorrow Thursday Feb 4

  18. Math 396-91 Page 125 allpage 126 allpage 127 all Finish for Tues Feb 9

  19. Workbook 306-05 page 122 Activity #1 Choice of two Options Page 124 #1 a,b,c,d using comparison method #2 a,b,c,d state the variables write the 2 rules find the answer using comparison Page 125 #3,4

  20. Math 396-92 Workbook page 127 #7 Page 129 Activity 3 Page 132 #5,6 Page 143 # 2,3 Page 144 #4,6,7 Page 145 #9 Page 146 #10,11,12 Finish for next wednesday When done: You may begin your honest numbers project.

  21. Page 145 #9 Rule A y = 300 zero Rule B y = 10x direct Rule C y = 5x + 100 partial

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