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Slide 2 Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy SubstitutionAddition Student Choice Special Systems Challenge Jeopardy Slide 3 $100 Question Substitution y = x + 2 y = 2x - 5 { Slide 4 $100 Answer Substitution (7, 9) Slide 5 $200 Question Substitution x = y - 1 x + 2y = 8 { Slide 6 $200 Answer Substitution (2, 3) Slide 7 $300 Question Substitution y = x 10 x 2y = 3 { Slide 8 $300 Answer Substitution (17, 7) Slide 9 $400 Question Substitution x y = -3 2x + y = 12 { Slide 10 $400 Answer Substitution (3, 6) Slide 11 $500 Question Substitution y x = 8 5x + 2y = 9 { Slide 12 $500 Answer Substitution (-1, 7) Slide 13 $100 Question Addition 3x + y = 6 5x y = 10 { Slide 14 $100 Answer Addition (2, 0) Slide 15 $200 Question Addition 3x + 2y = 10 3x 2y = 14 { Slide 16 $200 Answer Addition (4, -1) Slide 17 $300 Question Addition x + y = 12 2x + y = 6 { Slide 18 $300 Answer Addition (-6, 18) Slide 19 $400 Question Addition 3x y = 2 -8x + 2y = 4 { Slide 20 $400 Answer Addition (-4, -14) Slide 21 $500 Question Addition 2x = y + 20 3x + 2y = -19 { Slide 22 $500 Answer Addition (3, -14) Slide 23 $100 Question Student Choice y = 3 x 2x y = 6 { Slide 24 $100 Answer Student Choice (3, 0) Slide 25 $200 Question Student Choice -2x y = -5 3x + y = -1 { Slide 26 $200 Answer Student Choice (-6, 17) Slide 27 $300 Question Student Choice Slide 28 $300 Answer Student Choice Slide 29 $400 Question Student Choice y = x + 3 -2x + y = -4 Slide 30 $400 Answer Student Choice (7, 10) Slide 31 $500 Question Student Choice { 2x + y = 8 3x + 5y = 5 Slide 32 $500 Answer Student Choice (5, -2) Slide 33 $100 Question Special Systems y = 4 3x 3x + y = 4 { Classify and state the number of solutions. Slide 34 $100 Answer Special Systems Consistent and Dependent Infinitely Many Solutions Slide 35 $200 Question Special Systems 1.) What kinds of lines are inconsistent? 2.) Compare the slopes of the lines in an inconsistent system. 3.) Compare the y-intercepts of the lines in an inconsistent system. Slide 36 $200 Answer Special Systems 1.) Parallel 2.) The slopes are the same. 3.) The y-intercepts are different. Slide 37 $300 Question Special Systems y + 3x 2 = 0 9x + 3y = 6 { Classify and state the number of solutions. Slide 38 $300 Answer Special Systems Consistent and Dependent Infinitely Many Solutions Slide 39 $400 Question Special Systems { Classify and give the number of solutions. y + 3x = -1 x = y + 3x - 1 Slide 40 $400 Answer Special Systems Consistent and Independent One Solution Slide 41 $500 Question Special Systems { Classify and give the number of solutions. 3x 2y = 9 -6x + 4y = 1 Slide 42 $500 Answer Special Systems Inconsistent No Solution Slide 43 $100 Question Challenge 4x + y = 10 -2x = y + 4 { Solve twice. Use substitution AND addition. Slide 44 $100 Answer Challenge (7, -18) Slide 45 $200 Question Challenge y = 5/2x + 2 y = 2x + 4 { Solve by graphing. $50 BONUS Describe a real-life situation that could be represented by this data. Slide 46 $200 Answer Challenge (4, 12) One bowling alley charges $2.50 per game plus $2.00 for shoe rental. Another charges $2.00 per game plus $4.00 for shoe rental. For how many games will the cost of bowling be the same at both places. Slide 47 $300 Question Challenge 9x 2y = 15 4x + 3y = -5 Solve using addition. { Slide 48 $300 Answer Challenge (1, -3) Slide 49 $400 Question Challenge 2x 3y z = 12 y + 3z = 10 z = 4 { Slide 50 $400 Answer Challenge (5, -2, 4) Slide 51 $500 Question Challenge A group of students go out for lunch. If two have hamburgers and five have hot dogs, the bill will be $8.00. If five have hamburgers and two have hot dogs, the bill will be $9.50. What is the price of a hamburger? Slide 52 $500 Answer Challenge $1.50 Slide 53 Final Jeopardy The larger of two numbers is 1 more than twice the smaller. The sum of the numbers is 20 less than three times the larger. Find the two numbers. Slide 54 Final Jeopardy Answer 6 and 13 Slide 55 One cable television provider has a $60 setup fee and $80 per month, and the second has a $160 equipment fee and $70 per month. a.) In how many months will the cost be the same? What will that cost be. b.) If you plan to move in 6 months, which is the cheaper option? Explain. Slide 56 a.) 10 months, $860 b.) First company ($80/mo and $60 setup fee) $80(6) + $60 = $540 $70(6) + $160 = $580