# 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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