Question 983028
<pre>
{{{system(y=-2x+9,
y=expr(1/3)x+2)}}}

First we look at the first equation:

{{{y=-2x+9}}}

The slope is -2 which has a 1 denominator {{{(-2)/1}}}
The y-intercept is 9.  So we start at 9 on the y-axis
and go down 2 units (since it's negative) and go right 1 unit,
like this:

{{{drawing(400,400,-6,8,-3,11, graph(400,400,-6,8,-3,11),
line(0,9,0,7),line(0,7,1,7)  )}}} 

Then we take a ruler and draw a straight line through where
we started and where we ended, like this:

{{{drawing(400,400,-6,8,-3,11, graph(400,400,-6,8,-3,11),
line(0,9,0,7),line(0,7,1,7),
green(line(-14,37,15,-21))

  )}}} 

Now we look at the second line,

{{{y=expr(1/3)x+2}}}

The slope is {{{1/3}}}.  The y-intercept is 2.  So we start at 2
on the y-axis and go up 1 unit (since it's positive) and go right 
3 units,  like this:

{{{drawing(400,400,-6,8,-3,11, graph(400,400,-6,8,-3,11),
line(0,9,0,7),line(0,7,1,7), line(0,2,0,3),line(0,3,3,3),
green(line(-14,37,15,-21))

  )}}}

[Wow! that pokes right in to the other line!]  Then we take the
ruler and draw a straight line through where we started and where 
we ended, like this:

{{{drawing(400,400,-6,8,-3,11, graph(400,400,-6,8,-3,11),
line(0,9,0,7),line(0,7,1,7), line(0,2,0,3),line(0,3,3,3),
green(line(-14,37,15,-21),line(-12,-2,12,6))

  )}}}

Now we can tell where they cross.  Right there where that poked
into the first line.  If you draw a line straight down to the
x-axis, you see that the x-coordinate is 3.

{{{drawing(400,400,-6,8,-3,11, graph(400,400,-6,8,-3,11),
line(0,9,0,7),line(0,7,1,7), line(0,2,0,3),line(0,3,3,3),
green(line(-14,37,15,-21),line(-12,-2,12,6)), red(line(3,3,3,0))

  )}}}

There's already a line straight over the the y-axis, so you can
now see that the y-coordinate is also 3.  That means that the
solution is (x,y) = (3,3).

We can now check to make sure it's correct by substituting x=3 and 
y=3 in both original equations:

{{{system(y=-2x+9,
y=expr(1/3)x+2)}}}

{{{system(3=-2(3)+9,
y=expr(1/3)(3)+2)}}}

{{{system(3=-6+9,
3=1+2)}}}

{{{system(3=3,
3=3)}}}

So it checks.

Edwin</pre>