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Elimination Graphing Substitution Inequalities Potpourri 10 Point 10 Point 20 Points 20 Points 30 Points 30 Points 40 Points 40 Points 50 Points 50 Points

If you solve a system of linear equations and get 6 = 6 how many solutions does the problem have?

Infinitely many

Solve: 2 x + 5 y = 17 6 x – 5 y = -9

(1, 3)

Solve: 7 x + 2 y = 10 -7 x + y = -16

(2, -2)

Solve: 3 x + 2 y = -9 -10 x + 5 y = -5

(-1, -3)

A weekend at the Beach Bay Hotel in Florida costs $220 and includes 2 nights and 4 meals. A week includes 7 nights and 10 meals and costs $710. Let n = the cost of 1 night and m = the cost of 1 meal. Find the cost of 1 night and the cost of 1 meal.

One night: $80 One meal: $15

If you solve a system of equations by graphing and find out the lines are parallel, how many solutions does it have?

None

Solve: y = 2 x – 3 y= x-1

(2, 1)

Solve: y = -x + 4 x = -1

(-1, 5)

Solve: y = 3 x + 4 -12 x + 4 y = 16

Infinite solutions

Solve: 3 x + 4 y = 12 2 x + 4 y = 8

(4, 0)

Which point satisfies the system: y = 2 x + 5 2 x + 3 y = 31 A. (3, 5) B. C. (5, 7) B. (4, 13) D. (2, 9)

D. (2, 9)

Solve: y = 3 x – 4 y = -2 x + 1

(1, -1)

Solve: 4 x + 9 y = 24 y = -1/3 x + 2

(6, 0)

Solve: x=y+7 y = 8 + 2 x

(-15, -22)

A farmer grows only corn and beans on his 420 acre farm. He wants to plant 250 more acres of corn than of beans. How many acres of each crop does the farmer need to plant?

335 acres of corn, 85 acres of beans

Which point is not a solution of y < 2 x – 3 A. (5, 4) B. (3, 0) C. (4, 5) D. (1, -7)

C. (4, 5)

Which point is a solution to the system: y > 4 x – 1 y ≤ -x + 4 A. (3, 5) B. (1, 7) B. C. (2, 9) D. (-2, -2)

D. (-2, -2)

Solve by graphing: y ≥ -3 -3 x + y ≥ 6

Solve by graphing: y ≤ 2 x + 3 y > 2 x + 7

No solution

Write a system of inequalities for the following problem: You are going to sell Valentine kisses for $. 25 each and lollipops for $. 50 each. You want to sell at most 100 items, and you want to sell at least $50 worth of Valentine’s treats. Let x be the number of kisses, and y be the number of lollipops.

x + y ≤ 100. 25 x +. 50 y ≥ 50

If you solve a system of equations and get x=3 how many solutions does it have?

One

There are 24 questions on a test. Each question is worth either 4 points or 5 points. The test is worth a total of 100 points. Write and solve a system of equations.

x + y = 24 5 x + 4 y = 100 20 4 -point questions 4 5 -point questions

Solve using any method: 2 x + 3 y = 15 y = 2 x - 3

(3, 3)

Solve using any method: 2 x – 3 y = 8 2 x + 3 y = 8

(4, 0)

Solve using any method: y = 3 x – 6 x=y-2

(4, 6)

Make your wager

Suppose you invest $1500 in equipment to put pictures on t-shirts. You buy each t-shirt for $3. After you have placed the picture on a shirt, you sell it for $20. How many tshirts must you sell to break even?

89 t-shirts

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