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College Algebra

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For a test question, a mathematics teacher wants to find two constants a and b such that the test item "Simplify a(x + 2y) − b(2x − y)" will have an answer of -4x + 12y. What constants a and b should the teacher use?

  • College Algebra - ,

    a(x + 2y) − b(2x − y) = -4x + 12y
    ax + 2ay - 2bx + by = -4x + 12y
    x(a-2b) + y(2a + b) = -4x + 12y

    so a-2b = -4
    and 2a + b = 12

    first one times 2 ---> 2a - 4b = -8
    second one ----> 2a + b = 12
    subtract them: -5b = -20
    b = 4
    back in first: a - 8= - 4
    a = 4

    check:
    4(x+2y) - 4(2x-y)
    = 4x + 8y - 8x + 4y
    = -4x + 12y , checks!

  • College Algebra - ,

    awesome thanks!

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