Math

How many solutions does the system of equations have?
3x=-12y+15 and x + 4y=5

Y=6x+2 and 3y-18x=12

x-2y=6 and 3x – 6y =18

y-5x=-6 and 3y-15x=-12

Ok, so I’m having problems with these, so if Steve or Reiny could help with these problems and show the work for them that would help me study that would be great, however I need this done in 20 min. ( I know it’s bad having time limits) but unfortunately I need it done soon… so if you can help, awesome.

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  1. 3x=-12y+15 and x + 4y=5
    These two equations are the same. There is a y for any x.

    Y=6x+2 and 3y-18x=12
    3y = 18 x + 12 is y = 6 x + 4
    These are parallel lines that never intersect, no solution

    x-2y=6 and 3x – 6y =18
    again divide equation 2 by 3 and get
    x - 2 y - 6
    the two equations are the same, infinite solutions again

    y-5x=-6 and 3y-15x=-12
    divide second one by 3 and get
    y - 5 x = -4
    Again two parallel lines never cross, no solutions

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  2. Thank you Damon~!

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  3. Were they right?

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