What are the coordinates of the one point shared in common between the two linear functions give below?

Substitute 1 equation in the other

y = 2x-2 (1)
3y+x = 15 (2)

substitute (1) into (2)
3(2x-2)+x=15
6x-6+x=15
7x=21
x=3

now substitute x=3 into (1)
y =2(3)-2
y= 4

coordinates of point of intersection = (3,4)