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    Solving systems of equations

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    1. Solve by substitution or elimination method:
    3x - 2y = 8
    -12x + 8y = 32
    2. Solve by substitution or elimination method:
    7x - 5y = 14
    -4x + y = 27
    3. Solve by substitution or elimination method:
    -4x + 3y = 5
    12x - 9y = -15
    4. A university bookstore recently sold a wire bound graph-paper notebook for $2.50 and a college-ruled notebook for $2.30. At the start of spring semester, a combination of 50 of these notebooks was sold for a total of $118.60. How many of each type were sold?

    5. Write a system of equations for each of the following, and solve each of the systems.

    i. A unique solution.
    ii. An infinite number of solutions.
    iii. No solution.

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    https://brainmass.com/math/linear-algebra/solving-systems-of-equations-29253

    Solution Preview

    1. Solve by substitution or elimination method:
    3x - 2y = 8 (1)
    -12x + 8y = 32 (2)
    (1)*(-4): - 12x + 8y = -32 (3)
    (3) + (2): 0 = 0
    thus, (1) is equivalent to (2), there are infinite solutions.

    2. Solve by substitution or elimination method:
    7x - 5y = 14 (1)
    -4x + y = 27 (2)
    from (2): y = 4x+27 substitute into (1):
    7x - 5(4x+27) = 14
    7x-20x-135 = 14
    -13x = 149
    x = -149/13 = -11.46
    then y = 4x+27= 4(-11.46)+27 = ...

    Solution Summary

    This shows how to solve systems of equations using substitution or elimination.

    $2.49

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