#### Answer

{(2,1)}

#### Work Step by Step

x+3y=5
x+3y-3y=5-3y
x=5-3y
Plug this value for x into the other equation.
4(5-3y)+5y=13
4(5)-4(3y)+5y=13
20-12y+5y=13
20-7y=13
-7y=13-20
-7y=-7
y=$\frac{-7}{-7}$
y=1
Plug this back into the first equation to find x
x=5-3(1)
x=5-3
x=2
Therefore the solution is {(2,1)}