Math Help - graphing question connected with wolfram alpha

1. graphing question connected with wolfram alpha

hi, when i'm doing linear equations, i often check them on wolfram alpha. when i enter 2x+3y=6 it shows the line on the graph, solves for y BUT also lists the INTEGER SOLUTION. in this example it's

x=3n , y=-2(n-1)

how are these equations derived? thanks, any help appreciated

2. Originally Posted by damon
hi, when i'm doing linear equations, i often check them on wolfram alpha. when i enter 2x+3y=6 it shows the line on the graph, solves for y BUT also lists the INTEGER SOLUTION. in this example it's

x=3n , y=-2(n-1)

how are these equations derived? thanks, any help appreciated
Because $3$ and $6$ are both divisible by $3$ so must $x$ be. Put $x=3n$ for some $n \in \mathbb{Z}$, then:

$y=2(1-n)$

which is also in $\mathbb{Z}$ and you are done.

CB