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Math Help - Finding point of intersection algebraically

  1. #1
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    Finding point of intersection algebraically

    Another question for a test tomorrow that I don't understand... I know how to find the point of intersection for two lines on a graph easily but I don't understand how you do it algebraically and the teacher refuses to explain it to anyone again since we've already done it though I was absent that day.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ~NeonFire372~ View Post
    Another question for a test tomorrow that I don't understand... I know how to find the point of intersection for two lines on a graph easily but I don't understand how you do it algebraically and the teacher refuses to explain it to anyone again since we've already done it though I was absent that day.
    you set them equal to each other.

    say one line is y = 2x + 5 and the other is y = 3x - 1, then the (x-coordinate for the) point of intersection is given by:

    2x + 5 = 3x - 1

    do you see how that makes sense? we want to see where their y-values match up, and then match up the x-values at that point. if the x- and y-values are the same on both lines, it means it is a point they both pass through, and hence they intersect there
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  3. #3
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    2x + 5 = 3x - 1

    So I'd go:

    2x -3x = 5 - 1
    -1x = 4

    ... I'm really confused now.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ~NeonFire372~ View Post
    2x + 5 = 3x - 1

    So I'd go:

    2x -3x = 5 - 1
    -1x = 4

    ... I'm really confused now.
    that's because you did the wrong thing. first off, i'd move the x's to thee right hand side, to avoid the -x. it's no big deal really, but i like my math to look aesthetically pleasing.

    so, 2x + 5 = 3x - 1 .............subtract 2x from both sides.

    => 5 = 3x - 1 - 2x ..............simplify

    => 5 = x - 1 ......................now add 1 to both sides

    => 5 + 1 = x ......................simplify

    => x = 6

    thus we have found the x-coordinate for which the lines intersect. to find the y-coordinate, plug the x-value we found into either equation.

    say we decided to use y = 2x + 5

    plug in x = 6, we get:

    y = 2(6) + 5

    => y = 17


    say we decided to use y = 3x - 1

    plug in x = 6, we get:

    y = 3(6) - 1

    => y = 17 again, aha!

    so when x = 6, y = 17

    thus the point of intersection is (6,17)
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    Quote Originally Posted by Jhevon View Post
    that's because you did the wrong thing. first off, i'd move the x's to thee right hand side, to avoid the -x. it's no big deal really, but i like my math to look aesthetically pleasing.

    so, 2x + 5 = 3x - 1 .............subtract 2x from both sides.

    => 5 = 3x - 1 - 2x ..............simplify

    => 5 = x - 1 ......................now add 1 to both sides

    => 5 + 1 = x ......................simplify

    => x = 6

    thus we have found the x-coordinate for which the lines intersect. to find the y-coordinate, plug the x-value we found into either equation.

    say we decided to use y = 2x + 5

    plug in x = 6, we get:

    y = 2(6) + 5

    => y = 17


    say we decided to use y = 3x - 1

    plug in x = 6, we get:

    y = 3(6) - 1

    => y = 17 again, aha!

    so when x = 6, y = 17

    thus the point of intersection is (6,17)
    The two simplify steps - I don't get why the 5 would be = to the rest of it and why then it would be changed to =x.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ~NeonFire372~ View Post
    The two simplify steps - I don't get why the 5 would be = to the rest of it and why then it would be changed to =x.
    i did not change the 5 to x. i flipped the equation around. if i had simplified, i would have 6 = x, that looks weird, so i turned it around to say x = 6
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    But if you didn't simplify or flip anything around, how would it work?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ~NeonFire372~ View Post
    But if you didn't simplify or flip anything around, how would it work?
    what do you mean. nothing would change if we write 6 = x as opposed to x = 6. that's saying the same thing. i don't see your confusion i'm afraid. i simplify to make things look nicer and easier to use. like writing 6 instead of 5 + 1. they are the same thing, but one is simplified...
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