Question 747338
To use substitution, you need to solve for one of the variables in terms of the other.  I usually try to go for the easiest one, so I'm going to solve for x in the first equation.

{{{x+3y=15}}}

Subtract 3y from both sides:

{{{x=15-3y}}}

Now you have solved for x in terms of y.  
Next, use the OTHER equation, not the one you used to solve for x.

{{{2x-3y=3}}}

Plug in 15-3y for x.

{{{2(15-3y)-3y=3}}}

Distribute,

{{{30-6y-3y=3}}}

Combine like terms,

{{{30-9y=3}}}

Subtract 30 from both sides,

{{{-9y=-27}}}

Divide both sides by -9:

{{{y=3}}}


Now, plug in 3 for y into the equation where x is by itself.

{{{x=15-3y}}}

{{{x=15-3(3)}}}

{{{x=15-9}}}

{{{x=6}}}

Now you have x and y, so your answer is the ordered pair:
 
(6, 3)