Question 900830
<pre>
            {{{system(-5x+3y=12,x+2y=8)}}}

We look for a term in one of those equations that has a letter
with an understood coefficient of 1 or -1.

We see that {{{x+2y=8}}} has a term x with a 1 understood 
coefficient.  

We solve for that letter by getting it alone on one side:

            {{{x+2y=8}}}

Subtract 2y from both sides
                {{{x=8-2y}}}

Now in the other equation {{{-5x+3y=12}}}, substitute (8-2y)
for x

           {{{-5x+3y=12}}}
           {{{-5(8-2y)+3y=12}}}

Solve for y

           {{{-40+10y+3y=12}}}
           {{{-40+13y=12}}}
               {{{13y=12+40}}}
               {{{13y=52}}}
               {{{13y/13=52/13}}}
                {{{y=4}}}

Substitute (4) for y in the equation where you solved for x

                {{{x=8-2y}}}
                {{{x=8-2(4)}}}
                {{{x=8-8}}}
                {{{x=0}}}

So that means that the common solution to the pair of equations
is (x,y) = (0,4) 

It means that if you draw the graphs of the two lines they will
intersect at the point (0,4)

{{{system(-5x+3y=12,x+2y=8)}}}

{{{drawing(400,400,-10,10,-10,10,graph(400,400,-10,10,-10,10,(12+5x)/3),
graph(400,400,-10,10,-10,10,(x-8)/(-2)),
locate(.5,4.6,"(0,4)")

 )}}}

Edwin</pre>