Question 547239
There are a few ways to do this, depending on what variable you want to eliminate.  Just to make it simple, I will eliminate my r.  
{{{7r-3s=3}}}         (1)
{{{3r+7s=51}}}        (2)

I will multiply my equation (1) by 3 (the number in front of r in equation (2)), and my equation (2) by 7 (you guessed it.... the number in front of r in equation (1)).  This leaves:
{{{21r-9s=9}}}           (3)
{{{21r+49s=357}}}        (4)

Now Subtracting equation (4) by equation (3) we get:
{{{(21r-9s)-(21r+49s)=9-357}}}
{{{-9s-49s=-348}}}
{{{-58s=-348}}}
{{{-58s/-58=-348/-58}}}
{{{s=6}}}

Now we can substitute this value of s into any of the equations (1)-(4).  I will put it into equation (1).  
{{{7r-3*6=3}}}      
{{{7r-18=3}}} 
{{{7r-18+18=3+18}}}
{{{7r=21}}}  
{{{7r/7=21/7}}} 
{{{r=3}}}