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Math Help - equations system

  1. #1
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    Exclamation equations system

    ive been trying to answer these questions all night, 19 of them for homework and ive got 8 done. only 8 to go...

    10. Solve the following systems of equations by substitution. Show your work.
    a) y= 2x+10
    y = 130

    b) 2a + 3b = 35
    b=10


    c) 3x+5y = 12
    x+3y=6



    can someone explain to me how to do this, i dont understand it! i know how to check if their right afterwards, but especially for a.. i dont get what to 'plug in' and all that..
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  2. #2
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    For 10a), you're told y = 130. Take that value and plug it in for y in the first equation, y = 2x + 10.

    Replacing y by 130 gives 130 = 2x + 10. Solve for x by first subtracting 10 from both sides:

    120 = 2x.

    Now divide by 2; x = 60.

    Same idea for 10b) -- They tell you b = 10, so plug 10 in wherever you see b in the first equation, then solve for a.

    10c) is a little trickier.

    Take the second equation, x + 3y = 6, and solve it for one of the variables. You can choose either one, but this is easier to solve for x, since x isn't being multiplied by anything. This gives: x = 6 - 3y.

    Now that you know what x is (even though it's not a number, but still has y in it), take that and plug it in to the first equation. Wherever you see an "x", replace it by 6-3y, since they're the same thing.

    Your first equation, 3x + 5y = 12, now becomes:

    3(6-3y) + 5y = 12.

    Distribute on the left:

    18 - 9y + 5y = 12.

    Combine like terms.

    18 - 4y = 12.

    Now solve for y, first by subtracting 18 from both sides:

    -4y = -6

    And now divide by -4:

    y = 3/2.

    Plug that value in to EITHER equation and solve for x. I'll plug it in to the second equation, x + 3y = 6.

    This gives:

    x + 3(3/2) = 6, so

    x + 9/2 = 6.

    subtract 9/2 from both sides (think of 6 as 12/2) to get

    x = 3/2.

    That gives your answer: x = 3/2 and y = 3/2. It's just a coincidence that they both are the same value.
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