What is the common point of the lines y=20-x and 3x-2y-6=0 ?

To determine the common point of the lines, we'll have to
solve the system formed form the equations of the
lines.

y=20-x (1)

3x-2y-6=0
(2)

The solution of this system represents the coordinates
of the intercepting point.

We'll solve the system
using substitution method.

3x - 2(20-x) - 6 =
0 

We'll remove the
brackets:

3x - 40 + 2x - 6 =
0

We'll combine like tems:

5x
- 46 = 0

We'll add 46:

5x =
46

x = 46/5

We'll susbtitute x
in (1) and we'll have:

y=20 -
46/5

y = (100-46)/5

y =
54/5

The coordinates of the
intercepting point of the lines are (46/5 ,
54/5).