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Mathematics LibreTexts

11.1E: Systems of Linear Equations - Two Variables (Exercises)

  • Page ID
    56123
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    For the following exercises, determine whether the ordered pair is a solution to the system of equations.

    \(3 x-y=4\)

    1. \(\quad\) and (-1,1) \(x+4 y=-3\)
    \(6 x-2 y=24\)

    2. \(-3 x+3 y=18\)

    For the following exercises, use substitution to solve the system of equations.

    3
    \(10 x+5 y=-5\)
    \(3 x-2 y=-12\)

    4
    \(\frac{4}{7} x+\frac{1}{5} y=\frac{43}{70}\)
    \(\frac{5}{6} x-\frac{1}{3} y=-\frac{2}{3}\)

    5

    \(5 x+6 y=14\)
    \(4 x+8 y=8\)

    For the following exercises, use addition to solve the system of equations.

    6
    \(3 x+2 y=-7\)
    \(2 x+4 y=6\)

    7.

    \(3 x+4 y=2\)
    \(9 x+12 y=3\)

    8.

    \(8 x+4 y=2\)
    \(6 x-5 y=0.7\)

    For the following exercises, write a system of equations to solve each problem. Solve the system of equations.

    9. A factory has a cost of production \(C(x)=150 x+15,000\) and a revenue function \(R(x)=200 x\). What is the break-even point?

    10. A performer charges \(C(x)=50 x+10,000,\) where \(x\) is the total number of attendees at a show. The venue charges \(\$ 75\) per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?


    11.1E: Systems of Linear Equations - Two Variables (Exercises) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.