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Math Help - Solving Simultaneous Equations

  1. #1
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    Solving Simultaneous Equations

    I am doing some revision for my exams and I am really struggling with simultaneous equations. It's something I've never quite got my head around. I'm currently working through past papers and I've had a go at one of the questions, but there's no answers provided so I can't tell if I'm right or wrong. I reckon once I get my head around one I'll be fine with them.

    This is the question:

    When trying to solve the simultaneous equations 3x - y = 7 and 2x + 2y = 10 a student gets the answer x = 2, y = 2. For each of x and y, consider whether the value obtained is less than the correct value (too low), correct, or greater than the correct value (too high). Which of the following is true?

    (A) The value x = 2 is too low and the value y = 2 is correct
    (B) The value x = 2 is correct and the value y = 2 is too low
    (C) The value x = 2 is correct and the value y = 2 is too high
    (D) The value x = 2 is too high and the value y = 2 is too low
    (E) None of the above is true

    This is what I've done so far:

    6x - 2y = 14
    (6x - 2y) - 2x + 2y) = 4x = 14
    x = 14 / 4 = 3.5

    3 * 3.5 = 10.5
    3 * 3.5 - y = 7
    y = 3.5

    ...and now I'm stuck, I know I've gone wrong somewhere and I'm not quite sure where. I know there is the substitution method that I could try, but that's something I've never come across, although I might give it ago if it means I'll find it easier.

    Thanks for any help in advance
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  2. #2
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    Quote Originally Posted by Gall1987 View Post
    I am doing some revision for my exams and I am really struggling with simultaneous equations. It's something I've never quite got my head around. I'm currently working through past papers and I've had a go at one of the questions, but there's no answers provided so I can't tell if I'm right or wrong. I reckon once I get my head around one I'll be fine with them.

    This is the question:

    When trying to solve the simultaneous equations 3x - y = 7 and 2x + 2y = 10 a student gets the answer x = 2, y = 2. For each of x and y, consider whether the value obtained is less than the correct value (too low), correct, or greater than the correct value (too high). Which of the following is true?

    (A) The value x = 2 is too low and the value y = 2 is correct
    (B) The value x = 2 is correct and the value y = 2 is too low
    (C) The value x = 2 is correct and the value y = 2 is too high
    (D) The value x = 2 is too high and the value y = 2 is too low
    (E) None of the above is true

    This is what I've done so far:

    6x - 2y = 14
    (6x - 2y) - 2x + 2y) = 4x = 14
    x = 14 / 4 = 3.5

    3 * 3.5 = 10.5
    3 * 3.5 - y = 7
    y = 3.5

    ...and now I'm stuck, I know I've gone wrong somewhere and I'm not quite sure where. I know there is the substitution method that I could try, but that's something I've never come across, although I might give it ago if it means I'll find it easier.

    Thanks for any help in advance
    Your idea is sound but you have made a sign error

    E_1:3x-y=7
    E_2:2x+2y=10

    So first you multiply equation 1 by 2 to get

    E_3:6x-2y=14

    Now you add equation 3 to equation 2 to to get

    2x+2y+(6x-2y)=10+14 \iff 8x=24 \iff x=3

    Can you finish from here?
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  3. #3
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    I'll give it a go...

    I think you then put x = 3 in to equation 1?

    So 3 * 3 - y = 7
    Y = 2

    So the answer to the original question would be A (The value x = 2 is too low and the value y = 2 is correct)?
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by Gall1987 View Post
    I'll give it a go...

    I think you then put x = 3 in to equation 1?

    So 3 * 3 - y = 7
    Y = 2

    So the answer to the original question would be A (The value x = 2 is too low and the value y = 2 is correct)?
    Yes
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