Math

The graphs of 5x-3y=35, 7x-3y=43, and 4x-ay=61 all intersect at the same point. Find the value of "a".

Do I solve the systems and then plug in? I am not sure haha.

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  1. 5x-3y=35 7x-3y=43 solve simultaneously by subtracting 1 from 2:2x=8 x=8/2=4 5(4)-3y=35 -3y=35-20 y=15/-3=-5 since they intersect,x and y are similar:4(4)-a(-5)=61 5a=61-16 5a=45 a=9

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  2. Here is how I would have expected my students to show the steps:

    subtract the first equation from the second :
    7x-3y=43
    5x - 3y = 35
    2x = 8
    x = 4
    sub that back into 5x-3y=35
    20-3y=35
    -3y = 15
    y = -5

    So the first two lines intersect at (4,-5)
    But the third line of 4x-ay=61 also runs through that point, thus
    4(4) - a(-5) = 61
    16 + 5a = 61
    5a = 45
    a = 9

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