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Math Help - Hey guys Algebra 2 and strugling need help with these!!

  1. #1
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    Hey guys Algebra 2 and strugling need help with these!!

    Equation 1. 2x+2y=6
    y=3x+11
    Equation 2. 2x-6y=8
    y= -1/3x+2
    Equation 3. 6x+8y=4
    3x-5y=11
    Equation 4. 3x+5y=-18
    4x-2y=2
    Equation 5. 3x-2y+2z=5
    x+2y-z=2
    4x-y+3z=11
    Equation 6. slope= -3 through (4,-2) in slope intercept form

    Equation 7.Perpendicular to -2x+3y=12 through (-4,-5) in standard form

    Equation 8. x intercept of 6 through (-2,5) in slope intercept form

    Can anyone show me how to do these or atleast do one of each type like do number 1 number 4 number 6-8
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  2. #2
    Super Member Bacterius's Avatar
    Joined
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    Wellington
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    Answer

    These are linear systems. You can solve them with two methods : substitution and elimination. I hate the last one so I am going to explain substitution. It always works for linear systems and is quite easy and nice.
    Take your first system :

    2x+2y=6
    y=3x+11

    In the second equation, you know that y = 3x + 11. Therefore, in the first equation, you can change y to 3x + 11. Which gives :

    2x + 2(3x + 11) = 6
    2x + 6x + 22 = 6
    8x = -16
    x = -2

    You now know x, substitute it back into the second equation to find y :

    y = 3x + 11
    y = 3(-2) + 11
    y = -6 + 11
    y = 5

    Therefore the solutions are S = (-2 ; 5) Nice, eh ? (the brackets should be braces but I can't get them on the LaTex editor).
    Sometimes you will have to work a bit an equation so that one unknown is alone on a side of the equation (y = ...x... or x = ...y...) so that you can substitute easily.

    The three last systems, read your lessons on line equations and it should be easy to write a system of two equations and then solve it by substitution/elimination (the last one consists of adding or substracting the two equations to get rid of one unknown, but it doesn't always work).
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