The equations are
5x - 3y = - 11 ---------> (1)
3x + 22y = 1 ---------> (2)
Solve for x from (2)
3x = 1 - 22y
x = (1 - 22y)/3 ---------> (3)
Substitute x value in (1).
5[(1 - 22y)/3] - 3y = - 11
(5 - 110y - 9y)/3 = - 11
5 - 110y - 9y = - 33
5 - 119y = - 33
119y = 38
y = 38/119
⇒ y = 38/119.
Substitute y value in (3).
x = (1 - 22(38/119))/3 = - 239/119
⇒ x = - 239/119.
Solution of the system is x = - 239/119 and y = 38/119