Label the equations as follow:

2x+3y=15                      (1)

4x-3y=3                         (2)

Notice that 3y appears on the left-hand side of both equations.Adding the left-hand side of (1) and (2),and then the right-hand sides,gives:

2x+3y+4x-3y=15+3

6x=18

we have added equals to equals,and addition eliminates y.

substituting x=3 in (1) gives:

2X3+3y=15 =6+3y=15

6x+3y-6=15-6

3y=9

So,the solution is (3,3)