3.1E: Exercises - Solving Systems with Algebra
Solve the following problems.
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1) Determine if (0, 5) is a solution to the system. 6x - 2y = -10 3x + y = 8 |
2) Determine if (-3, 2) is a solution to the system. -4x - 3y = 6 2x + 5y = 4 |
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3) Solve this system using graphing. y = 3x + 4 y = 5x - 2 |
4) Solve this system using graphing. x - 2y = -6 y = -2x - 7 |
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5) Solve this system using substitution. y = 3x - 1 2x + y = 4 |
6) Solve this system using substitution. 2x + y = 9 3x - 2y = -4 |
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7) Solve this system using elimination by addition. 3x - 7y = -1 2x + 7y = -24 |
8) Solve this system using elimination by addition. 2x - 3y = 4 3x - 4y = 5 |
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9) The supply and demand curves for a product are: Supply y = 2000x - 6500
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10) The supply and demand curves for a product are
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11) A car rental company offers two plans for one way rentals.
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12) A demand curve for a product is the number of items the consumer will buy at different prices. At a price of $2 a store can sell 2400 of a particular type of toy truck. At a price of $8 the store can sell 600 such trucks. If x represents the price of trucks and y the number of items sold, write an equation for the demand curve. |
13) A supply curve for a product is the number of items that can be made available at different prices. A manufacturer of toy trucks can supply 2000 trucks if they are sold for $8 each; it can supply only 400 trucks if they are sold for $4 each. If x is the price and y the number of items, write an equation for the supply curve. |
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14) The equilibrium price is the price where the supply equals the demand. From the demand and supply curves obtained in the previous two problems, find the equilibrium price, and determine the number of items that can be sold at that price. |
15) A break-even point is the intersection of the cost function and the revenue function, that is, where total cost equals revenue, and profit is zero. Mrs. Jones Cookies Store's cost and revenue, in dollars, for x number of cookies is given by C = .05x + 3000 and R = .80x. Find the number of cookies that must be sold to break even. |
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16) A company's revenue and cost in dollars are given by R = 225x and C = 75x + 6000, where x is the number of items. Find the number of items that must be produced to break-even. |
17) A firm producing socks has a fixed cost of
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18) Whackemhard Sports is planning to introduce a new line of tennis rackets. The fixed costs for the new line are $25,000 and the variable cost of producing each racket is $60.
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19) It costs $1,200 to produce 50 pounds of a chemical and it costs $2,200 to produce 150 pounds. The chemical sells for $15 per pound
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