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1.4E: Exercises - Solving Systems of Linear Equations in Two Variables

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    147277
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    Solve the following problems.

    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

    3) Solve this system using graphing.

    y = 3x + 4

    y = 5x - 2

    4) Solve this system using graphing.

    x - 2y = -6

    y = -2x - 7

    5) Solve this system using substitution.

    y = 3x - 1

    2x + y = 4

    6) Solve this system using substitution.

    2x + y = 9

    3x - 2y = -4

    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

    9) The supply and demand curves for a product are: Supply y = 2000x - 6500
    Demand y = - 1000x + 28000,
    where x is price and y is the number of items. At what price will supply equal demand and how many items will be produced at that price?

    10) The supply and demand curves for a product are
    Supply y = 300x - 18000 and
    Demand y = - 100x + 14000,
    where x is price and y is the number of items. At what price will supply equal demand, and how many items will be produced at that price?

    11) 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.

    12) 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.


    This page titled 1.4E: Exercises - Solving Systems of Linear Equations in Two Variables is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Rupinder Sekhon and Roberta Bloom via source content that was edited to the style and standards of the LibreTexts platform.