Answer
$(0,0)$ is a solution,
$(1,\displaystyle \frac{1}{3})$ is not a solution,
$(2,-\displaystyle \frac{2}{3})$ is a solution.
Work Step by Step
An ordered pair (a,b) is a solution of an equation in x and y if,
substituting a for x and b for y,
we obtain an equation that holds true.
Another way of stating this is that (a,b) satisfies the equation.
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$(x,y)=(0,0)$
$(0)+3(0)=0$
$0+0=0 \qquad $.... true, a solution
$(x,y)=(1,\displaystyle \frac{1}{3})$
$(1)+3(\displaystyle \frac{1}{3})=0$
$1+1=0 \qquad $.... false, not a solution
$(x,y)=(2,-\displaystyle \frac{2}{3})$
$(2)+3(-\displaystyle \frac{2}{3})=0$
$2-2=0 \qquad $.... true, a solution
