Posted by Neil on Wednesday, October 3, 2012 at 3:31pm.
I will do #3, you try the others
3.
2x - 6y = -2
x = 3y-1
sub into the 1st:
2(3y-1) - 6y = -2
6y - 2 - 6y = -2
0 = 0
Ahhh, since the variables dropped out and we ended up with a TRUE statement, the two equations are really one and the same equation.
(if you simplify the first, you get the second ...
2x - 6y = -2
divide by 2
x - 3y = -1
x = 3y - 1, which was the second equation )
So any ordered pair which satisfies the 1st will obviously also satisfy the second.
Had we ended up with a false statement, such as 3 = 0, there would have been no solution at all
Hm... so, 0=0 is the only answer for #3? You don't have to do anything else? Like plugging in for the second equation or something.
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