To solve the system of equations 2x - 3y = 22 and 3x + 2y = 7, we can use the method of elimination.
Multiplying the first equation by 2 and the second equation by 3, we get:
4x - 6y = 44 (1)
9x + 6y = 21 (2)
Adding equations (1) and (2), we get:
13x = 65
Dividing both sides by 13, we get:
x = 5
Substituting x = 5 into the second equation, we get:
3(5) + 2y = 7
Simplifying:
15 + 2y = 7
Subtracting 15 from both sides, we get:
2y = -8
Dividing both sides by 2, we get:
y = -4
Therefore, the solution to the system of equations is x = 5 and y = -4, which corresponds to option (D).