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How many solutions exist between a pair of parallel lines? ~50~ How many solutions exist between a pair of parallel lines? A. No Solution C. Two Solutions B. One Solution D. Infinite Solutions

~50~ ANSWER A. No Solution

Solve by graphing: X + Y = 6 3X - 4Y = 4 ~100~ Solve by graphing: X + Y = 6 3X - 4Y = 4 A. (-2, -4) C. (-4, -2) B. (2, 4) D. (4, 2)

~100~ ANSWER D. (4, 2)

Solve by substitution: y = 3x - 12 2x + 3y = -3 ~200~ Solve by substitution: y = 3x - 12 2x + 3y = -3 A. (3, -3) C. (0, 1) B. (-6, 6) D. (6, 6)

~200~ ANSWER A. (3, -3)

Solve by elimination: 2x - 5y = 1 3x - 4y = -2 ~400~ Solve by elimination: 2x - 5y = 1 3x - 4y = -2 A. (-1, -2) C. No solution D. Infinite Solutions B. (-2, -1)

~400~ ANSWER B. (-2, -1)

~500~ Open Ended: State how you determine if a system of equations has no solution or infinite solutions without graphing.

~500~ ANSWER Look at the slopes in the equations. If they are the same, the lines are parallel. If they are opposite reciprocals, the lines are perpendicular.

~650~ Write a system of equations for the following: The sum of two numbers is 7. Four times the first number is one more than five times the second. C. x + y = 7 5x = 4y + 1 A. x + y = 7 4x = 5y - 1 B. x + y = 7 4x + 1 = 5y D. x + y = 7 4x = 5y + 1

~50~ ANSWER D. x + y = 7 4x = 5y + 1

Solve and check: 5a - 2b = 3 2a - b = 0 ~800~ Solve and check: 5a - 2b = 3 2a - b = 0 A. a = 6 b = 3 C. a = 3 b = 6 B. a = -3 b = -6 D. a = 3 b = -6

~800~ ANSWER C. a = 3 b = 6

~1000~ Misha has a 2500 meter spool of rope that he must cut into 50 meter and 75 meter lengths for his rock climbing class. Write an inequality that will express the possible numbers of each length he can cut from this spool of rope. A. 50x + 75y  2500 C. 2500/50x ≤ 75y B. 50x + 75y ≤ 2500 D. 50x ≥ 2500 - 75y

~1000~ ANSWER B. 50x + 75y ≤ 2500

~1200~ A company produces windows and doors. A profit of $5 is realized on each window, an $3 on each door. The company has 18 hours available for manufacturing at plant A where it takes 3 hours for each window and 2 hours for each door. Plant B has 7.5 hours available for assembly where it takes 1.5 hours for each window, and .75 hours for each door. Write a system to model this problem. 3x + 1.5 y ≤ 18 2x + .75y ≤ 7.5 5x + 3 y ≤ 18 2x + 1.5y ≤ 7.5 A. C. 3x + 2y ≤ 18 1.5x + .75y ≤ 7.5 You can’t write a system for this problem. B. D.

~1200~ ANSWER 3x + 2y ≤ 18 1.5x + .75y ≤ 7.5 B.

How many solutions does this system have? 2x - 3y = 11 6x - 9y = 33 ~1500~ How many solutions does this system have? 2x - 3y = 11 6x - 9y = 33 A. One C. Infinite B. Two D. None

~1500~ ANSWER C. Infinite

~1750~ Write an equation of the line that is parallel to y= 3x-4 and passes through point (0,-3). A. Y = 3x – 0 C. Y = 4x - 3 B. Y = 3x – 3 D. Y = 3x + 3

~1750~ ANSWER B. Y = 3x – 3

~2000~ Write the equation of the line through (4,5) and perpendicular to the line with equation 3x + 2y = -1. A. Y = 3x + 2 C. y = -5x + 1/2 D. y = 4x + 5 B. y = -3/2x – 1/2

~2000~ ANSWER B. y = -3/2x – 1/2

Which equation is parallel to the graphed line? ~2100~ Which equation is parallel to the graphed line? A. Y = 4/5x + 2 C. Y = 5/4x + 2 B. Y = -5/4x + 2 D. Y = -4/5x + 2

~2100~ ANSWER A. Y = 4/5x + 2

~2250~ A small fast food restaurant invests $5,000 to produce a new food item that will sell for $3.49 each. Each item can be produced for $2.16. How many items must be sold to break even? A. 885 items C. 1433 items B. 2315 items D. 3760 items

~2250~ ANSWER D. 3760 items

~2500~ OPEN ENDED: A ticket office sells reserved tickets and general admission tickets to a rock concert. The auditorium normally holds no more than 5000 people. There can be no more than 3000 reserved tickets and no more than 4000 general admission tickets sold. Write a system of inequalities to represent the possible combinations of reserved tickets and general admission tickets that can be sold.

~2500~ ANSWER X + y ≤ 5000 X ≤ 3000 Y ≤ 4000

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