algebra

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addition method:3x-5y=-2 and 5y-2x=-2
how would I solve it since they are not together?

  • algebra -

    These simultaneous equations can be solved most of the time by either substitution or by elimination. We will try elimination here, since I see 5y in both equations.

    3x-5y=-2....(1)
    5y-2x=-2....(2)
    Rearrange to line up x and y in columns
    3x-5y=-2...(1a)
    -2x+5y=-2...(2a)
    Add the two equations:
    3x-2x -5y+5y = -2 -2
    simplify to get
    x = -4 ... (3)

    Substitute (3) into (1) to get
    3(-4)-5y=-2
    -5y = -2 + 12
    -5y = 10
    y = 10 / (-5) = -2 ..(4)

    (3) and (4) give the final answer, but we still have one more step to do: check!

    Substitute (3) and (4) into (1) and (2) to get
    3(-4)-5(-2)
    =-12+10
    =-2 from (1) OK

    5(-2)-2(-4)
    =-10+8
    =-2 from (2) OK

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