Thread: 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

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 $\displaystyle 3$ and $\displaystyle 6$ are both divisible by $\displaystyle 3$ so must $\displaystyle x$ be. Put $\displaystyle x=3n$ for some $\displaystyle n \in \mathbb{Z}$, then:

$\displaystyle y=2(1-n)$

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

CB