Systems Of Linear Equations … and other stuff

Please select a Team. Team 1 Team 2 Team 3 Team 4 Team 5 1 2 3 4 5

Tell whether the system has no solution, one solution, or infinitely many solutions.

y = 5x– 4 y = 5x– 5 no solutions one solution infinitely many solutions 1 2 3 4 5

y = x + 4 y – 4 = x no solutions Infinitely many solutions one solution 1 2 3 4 5

y = 2x – 3 y = –x + 3 one solution no solutions infinitely many solutions 1 2 3 4 5

Team Scores Team 1 Team 2 Team 3 Team 4 Team 5

Solve the following systems of equations .... … if you can.

y = 2x + 3 y = 3x + 1 (–2, –1) (–1, –2) (2, 7) (–2, –5) 1 2 3 4 5

Solve by substitution. y = 2x – 10 y = 4x – 8 (3, 4) (–1, –12) (–4, –17) (3, –4) 1 2 3 4 5

3y = –x + 2 y = –x + 9 (3, 6) (20, –4) (10, –1) (–1, 8) 1 2 3 4 5

Team Scores Team 1 Team 2 Team 3 Team 4 Team 5

y = 4x + 6 y = 2x (1, 2) (3, 6) (6, 3) (-3,-6) 1 2 3 4 5

The length of a rectangle is 2 cm more than four times the width The length of a rectangle is 2 cm more than four times the width. If the perimeter of the rectangle is 84 cm, what are its dimensions? length = 8 cm; width = 34 cm length = 34 cm; width = 8 cm length = 30 cm; width = 10 cm length = 34 cm; width = 10 cm 1 2 3 4 5

Find the value of b that makes the system of equations have the solution (3, 5). y = 3x – 4 y = bx + 2 –1 2 1 1 2 3 4 5

Team Scores Team 1 Team 2 Team 3 Team 4 Team 5

x + y = 8 2x – y = 24 48 and 24 x – y = 8 2x + y = 24 52 and 30 The sum of two numbers is 82. Their difference is 24. Write a system of equations that describes this situation. x + y = 8 2x – y = 24 48 and 24 x – y = 8 2x + y = 24 52 and 30 x + y = 24 y – x = 82 48 and 30 x + y = 8 2x – y = 24 53 and 29 1 2 3 4 5

4 five-dollar bills, 10 one-dollar bills Sharon has some one-dollar bills and some five-dollar bills. She has 14 bills. The value of the bills is $30. Solve a system of equations using elimination to find how many of each kind of bill she has. 4 five-dollar bills, 10 one-dollar bills 3 five-dollar bills, 10 one-dollar bills 5 five-dollar bills, 5 one-dollar bills 5 five-dollar bills, 9 one-dollar bills 1 2 3 4 5

Solve by elimination. 6x + 3y = –12 6x + 2y = –4 (10, –16) (2, –8) (–2, 8) (–10, 16) 1 2 3 4 5

3x + 3y = –93 x – 3y = 21 (3, –6) (–5, 2) (3, 3) (2, –5) 1 2 3 4 5

Team Scores Team 1 Team 2 Team 3 Team 4 Team 5

Which method is best for solving this system of equations Which method is best for solving this system of equations? 2x – 2y = –8 x + 2y = –1 Substitution Elimination Graphing magic 1 2 3 4 5

2x – 2y = –8 x + 2y = –1 (–14, 1) (1, 5) (–3, 1) (0, 4) 1 2 3 4 5

3x – 4y = –24 x + y = –1 (–4, 3) (0, 6) (3, 4) (4, 3) 1 2 3 4 5

Team Scores Team 1 Team 2 Team 3 Team 4 Team 5

x + 2y = –63 x + 8y = –20 (–1, –4) (–4, 4) (–4, –1) (3, 1) 1 2 3 4 5

5x = –25+ 5y 10y = 42+ 2x (–1, 2) (–1, 4) (4, –1) (5, 10) 1 2 3 4 5

–10x – 3y = –18 –7x – 8y = 11 (–7, –10) (–4, 3) (3, –4) (2, –1) 1 2 3 5

3x – 4y = 9 –3x + 2y = 9 (3, 9) (–27, –9) (–3, –6) (–9, –9) 1 2 3 4 5

Team Scores Team 1 Team 2 Team 3 Team 4 Team 5

30 nickels and 28 dimes 31 nickels and 29 dimes A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is $4.45. Find the amount of nickels and dimes that are in the jar. 30 nickels and 28 dimes 31 nickels and 29 dimes 29 nickels and 31 dimes 30 nickels and 32 dimes 1 2 3 4 5

By what number should you multiply the first equation to eliminate the x ? –3x – 2y = 2 –9x + y = 5 6 –9 2 3 1 2 3 4 5

An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates. John paid the admission fees for his six nephews and rented five pairs of ice skates. He was charged $32.00. Juanita paid the admission fees for her seven grandchildren and rented five pairs of ice skates. She was charged $35.25. What is the admission fee? What is the rental fee for a pair of skates? admission fee: $3.25 skate rental fee: $2.50 admission fee: $3.50 skate rental fee: $3.00 admission fee: $3.00 skate rental fee: $2.00 admission fee: $4.00 skate rental fee: $3.50 1 2 3 4 5

Team Scores Team 1 Team 2 Team 3 Team 4 Team 5

196 copies 301 copies 300 copies 195 copies You decide to market your own custom computer software. You must invest $3,255 for computer hardware, and spend $2.90 to buy and package each disk. If each program sells for $13.75, how many copies must you sell to break even? 196 copies 301 copies 300 copies 195 copies 1 2 3 4 5

Mike and Kim invest $14,000 in equipment to print yearbooks for schools. Each yearbook costs $7 to print and sells for $35. How many yearbooks must they sell before their business breaks even? 650 2,000 500 400 1 2 3 4 5

Team Scores Team 1 Team 2 Team 3 Team 4 Team 5

Last question! Worth 10,000 points … … no pressure!

A motorboat can go 8 miles downstream on a river in 20 minutes A motorboat can go 8 miles downstream on a river in 20 minutes. It takes 30 minutes for the boat to go upstream the same 8 miles. Find the speed of the current. 7 mph 6 mph 5 mph 4 mph 1 2 3 4 5

Team Scores Team 1 Team 2 Team 3 Team 4 Team 5