Substitute 2x-3y = -3 and 5x + 2y = 5 for the system of equations

We select from the first equation x:
2x-3y = -3; 2x = 3y-3;
x = (3y-3) / 2;
Substitute the resulting value into the second equation and find y:
5 * (3y-3) / 2 + 2y = 5;
15y / 2-15 / 2 + 2y = 5;
19y / 2 = 10/2 + 15/2 = 25/2;
y = 25/2 * 2/19 = 25/19;
Find x:
x = (3 * 25 / 19-3) / 2;
x = 75 / 38-3 / 2 = 75 / 38-57 / 38 = 18/38 = 9/19.
Answer: y = 25/19; x = 9/19.