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Math Help - linear systems (please help...exam is coming up!)

  1. #1
    Junior Member
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    linear systems (please help...exam is coming up!)

    i actually dont know if this goes here, so my apologies.
    but i need to know how to solve these linear systems problems, they're hte only ones i dont get. its my exam review and my math exam is this week!

    1. Mr Kay invested $5000, part at 6% and the rest at 9%. After one year, the interest from the money invested at 6% was 210$ more than the interest from the money invested at 9%. How much money was invested at each rate?

    2. Travelling with the wind, a plane flew 600 km from Aker to Beeton in 2h. On the return trip, travelling against the wind, the plane took 3h. Find the speed of the plane and the wind.

    also, i am horrible at fractions:

    Solve.
    a) x - y/3 = -1
    2/3x - 1/4y = -1

    b) m/3 - n/6 = 1/2
    1/5(m) - 3/10 (n) = 1/2

    thanks in advance.
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  2. #2
    Senior Member
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    Quote Originally Posted by checkmarks View Post
    Solve.
    a) x - y/3 = -1
    2/3x - 1/4y = -1

    b) m/3 - n/6 = 1/2
    1/5(m) - 3/10 (n) = 1/2
    a.)

    Consider the augmented matrix:

    Matrix A := [[1, -1/3, -1],[2/3, -1/4, -1]]

    Multiply -2/3 times row 1 (R_1) and add to R_2.

    Thus, we have: [[1, -1/3, -1],[0, -1/36, -1/3]]

    Multiply R_2 by -12 and add to R_1.

    [[1, 0, 3],[0, -1/36, -1/3]]

    Divide R_2 by -1/36

    [[1, 0, 3],[0, 1, 12]]

    Thus, we have reduced echelon form, where x_ 1 = 3 and x_2 = 12 (or in your case, x and y, respectively).

    I'll let you check to see that it works.

    b.) Try it- if you get stuck show what you attempted and we can probably show where you went wrong.
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  3. #3
    Junior Member
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    Dec 2006
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    thank you.
    can anyone help me with the word problems though? please? my exam is tmrw.
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