Question

How many solutions does the following system have?
y = -2/3 x + 3 and 2x + 3y = 9

Answer 1

get them in the same form
(2/3)x+y=3
2x+3y=9
lets get rid of the fraction on the first equation by multiplying each term by 3
we now have
2x+3y=9
and our second equation is
2x+3y=9
they are the exact same thing
so they are the same line, so there are infinite solutions because there are infinite solutions to a line, and what ever satisfies the first line of course satisfies the second line

Answer 2

Alright that makes sense, thanks!