Question 62413
Yes your idea is correct.

Equation 1 : 2x - 3y = 0 
Equation 2 : 3x + 2y = 13

Multiply the first equation by 2 and the second equation by 3. This will give a -6y in the first equation and a 6y in the second equation which can easily be eliminated.

New Equation 1 : 4x - 6y = 0 
New Equation 2 : 9x + 6y = 39

Add the two equations together to get
13x = 39

Obviously x must be 3. Substitute x=3 into one of the two equations.
2*3 - 3y = 0 
6=3y ie y must be 2
Therefore x + y = 3 + 2 = 5