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**Jeopardy 100 200 300 400 500 Solve Systems 1 Solve Systems 2**

Special Types of Systems Systems of Inequalities Extensions 100 200 300 400 500

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**Solve the linear system by graphing:**

100 Solve the linear system by graphing: 6x – 3y = 36 5x = 3y + 30

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200 One day, you are rollerblading on a trail while it is windy. You travel along the trail, turn around and come back to your starting point. On your way out on the trail, you are rollerblading against the wind. On your return trip, which is the same distance, you are rollerblading with the wind. You can only travel 3 miles an hour against the wind, which is blowing at a constant speed. You travel 8 miles an hour with the wind. Write and solve a system of equations to find the average speed when there is no wind and the speed of the wind.

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300 A drummer is stocking up on drum sticks and brushes. The wood sticks that he buys are $10.50 a pair and the brushes are $24 a pair. He ends up spending $90 on sticks and brushes and buys two times as many pairs of sticks as brushes. How many pairs of sticks and brushes did he buy?

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400 You bought 15 one-gallon bottles of apple juice and orange juice for a school dance. The apple juice was on sale for $1.50 per gallon bottle. The orange juice was $2 per gallon bottle. You spent $26. Write a system of equation and then graph it. How many bottles of each type of juice did you buy?

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500 The area of the room shown is 224 square feet. The perimeter of the room is 64 feet Find x and y.

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**Solve the linear system:**

100 Solve the linear system: y – 3 = –2x 2x + 3y = 13

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200 A fishing barge leaves from a dock and moves upstream (against the current) at a rate of 3.8 miles per hour until it reaches its destination. After the people on the barge are done fishing, the barge moves the same distance downstream (with the current) at a rate of 8 miles per hour until it returns to the dock. The speed of the current remains constant. Write and solve a system of equations to find the average speed of the barge in still water and the speed of the current.

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300 You will be making hanging flower baskets. The plants you have picked out are blooming annuals and non-blooming annuals. The blooming annuals cost $3.20 each and the non-blooming annuals cost $1.50 each. You bought a total of 24 plants for $ Write a linear system of equations that you can use to find how many of each type of plant you bought.

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400 A total of $45,000 is invested into two funds paying 5.5% and 6.5% annual interest. The combined annual interest is $2725. How much of the $45,000 is invested in each type of fund? Write and solve a system of equations.

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500 A rectangular hole 3 centimeters wide and x centimeters long is cut in a rectangular sheet of metal that is 4 centimeters wide and y centimeters long. The length of the hole is 1 centimeter less than the length of the metal sheet. After the hole is cut, the area of the remaining metal sheet is 20 square centimeters. Find the length of the hole and the length of the metal sheet.

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100 Without solving the linear system, tell whether the linear system has one solution, no solution, or infinitely many solutions. 4y =12x –1 –12x + 3y = –1

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200 Without solving the linear system, tell whether the linear system has one solution, no solution, or infinitely many solutions. –2x + 3y = 4 3x – 2y = 5

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300 Without solving the linear system, tell whether the linear system has one solution, no solution, or infinitely many solutions. 5y –4x = 3 10y = 8x + 6

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400 Without solving the linear system, tell whether the linear system has one solution, no solution, or infinitely many solutions. 3y + 5x = 1 –5x –3y = 1

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500 Without solving the linear system, tell whether the linear system has one solution, no solution, or infinitely many solutions. –3x + 4y = 24 4x + 3y = 2

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**Graph the system of inequalities.**

100 Graph the system of inequalities. x ≥ 0 y ≥ 0 2x + y < 3

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**Graph the system of inequalities.**

200 Graph the system of inequalities. x > 4 x < 8 y ≥ 2x + 1

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**Write a system of inequalities for the shaded region.**

300 Write a system of inequalities for the shaded region.

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**Write a system of inequalities for the shaded region.**

400 Write a system of inequalities for the shaded region.

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**Graph the system of inequalities.**

500 The tickets for a school play cost $8 for adults and $5 for students. The auditorium in which the play is being held can hold at most 525 people. The organizers of the school play must make at least $3000 to cover the costs of the set construction, costumes, and programs. Write a system of linear inequalities for the number of each type of ticket sold. Graph the system of inequalities. If the organizers sell out and sell twice as many student tickets as adult tickets, can they reach their goal?

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**Solve the following system using Cramer’s Rule.**

100 Solve the following system using Cramer’s Rule. 9x – 4y = –55 3x = –4y – 21

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**Write a system of inequalities formed by the vertices:**

200 Write a system of inequalities formed by the vertices: (2, 2), (-2, 4) and (-1, -3)

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**Solve the following system using Cramer’s Rule.**

300 Solve the following system using Cramer’s Rule. x – y = 0 2x + 4y = 18

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**Write a system of inequalities formed by the vertices:**

400 Write a system of inequalities formed by the vertices: (-1, 1), (2, 2), (3, -2) and (-4, -3)

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**Solve the following system using Cramer’s Rule.**

500 Solve the following system using Cramer’s Rule. y = –2x + 4 5y – 2x = –16

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A system of linear equations allows the relationship between two or more linear equations to be compared and analyzed. 4.1 - Systems of Linear Equations.

A system of linear equations allows the relationship between two or more linear equations to be compared and analyzed. 4.1 - Systems of Linear Equations.

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