Math

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12x+4y= 22 and 3x-8y= -10
What are the coordinates of x and y? Use the Substitution Method.
---and---
-5x+7y= -41 and 7x+y=25
What are the coordinates of x and y? Use the Substitution Method.

Please help!!! =DDD

  • Math -

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    Homework Help Forum: Math
    Current Questions | Post a New Question | Answer this Question | Further Reading

    Posted by Catherine on Friday, January 25, 2008 at 9:27pm.

    12x+4y= 22 and 3x-8y= -10
    What are the coordinates of x and y? Use the Substitution Method.
    For the first one.
    12x+4y=22
    3x-8y=-10
    =============
    I would solve equation 2 for x as
    x=(-10+8y)/3
    Then substitute this for x in equation 1 as
    12[(-10+8y)/3] + 4y = 22
    4(-10+8y) + 4y = 22
    -40 + 32y + 4y = 22
    36y = 40 + 22
    36y = 62 + 40 = 62
    y = 62/36 = 31/18
    a strange number but it's right I think.
    You substitute this value for y into equation 2 and solve for x. I found x to be 34/27, another strange number, but I think it's right. That's how you do these things. I'll leave the other one for you. Post specific questions if you get stuck. By the way, I substituted 31/18 for x and 34/27 for y and it checks. Check my work,especially for typos.
    y = 30/36 =
    ---and---
    -5x+7y= -41 and 7x+y=25
    What are the coordinates of x and y? Use the Substitution Method

  • Math -

    I don't know why my post copied all that extra trash but the part you want to read is in bold (except for the last y = 30/36 which has nothing to do with your problem). I'm pleased that Damon obtained the same strange numbers I did.

  • Math -

    12x+4y= 22 and 3x-8y= -10
    These are both equations of lines and if they are not the same or parallel they will cross each other at one point, giving you a spot with x, y coordinates.
    To solve it by substitution, solve either equation for either x or y and use that in the other equation. Then go back and find the value of the substituted variable with either original.
    For example:
    1.
    solve the first equation for y
    4 y = -12 x + 22
    so
    y = (-3 x + 11/2)

    2.
    Use that y in your second equation to get x
    3 x - 8(-3x + 11/2) = -10
    3 x + 24 x - 44 = -10
    27 x = 34
    x = 34/27

    3.
    use x = 34/27 in either original, like the first, to get y
    12 (34/27) + 4 y = 22
    136/9 + 4 y = 22
    4 y = 62/9
    y = 31/18

    So, our intersection point is (34/27,32/18)

  • Math -

    I checked the strange numbers back. They worked.

  • Math -

    I did too because I didn't believe them (until I checked).

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