How would you solve this by elimination?

To solve this equation by elimination, what you would do is multiply one of the equations by -1, or distribute -1 to each term in the equation, any of the 2 equations. Then align the equations and add them together.

-(X + 3y = 3)
-X - 3y = -3

-X - 3y = -3
X + 6y = 3

3y = 0
y = 0/3 = 0.

Now we can solve for x, by simply plugging the value of y into any of the 2 equations.

X + 6y = 3
X + 6(0) = 3
X + 0 = 3
X = 3.

The solution to your system of equations would be (3,0).

Check this by plugging in the point to the other equation and see if it is true.

X + 3y = 3
(3) + 3(0) = 3
3 + 0 = 3
3 = 3.

Thus it is the solution.