Question 972273
3x+2y=54 
2x-3y=10

Multiply the first by 3 and the second by 2:

9x +6y = 162
4x - 6y= 20   Now add them.  The y s add to 0.

13x  ;;;   = 182   Divide by 13.
x=14
Substitute back in to the first

42 +2y =54
2y=12
y=6

Try the second equation to check.
28-18=10

(14,6) is the solution.