The given equations are :

3x+7y = 20....(1)

x-7y = 4.........(2).

From (2) , x = 4+7y. Substitute x = 4+7y in (1):

3(4+7y) +7y = 20.

12+21y+7y = 20.

28y = 20-12 = 8.

y = 8/21 = 8/28.

Substitute y = 2/7 in (2):

x -7(2/7) = 4.

x-2 = 4.

x = 4+2 = 6

Therefore x = 6 and y = 2/7.

To determine the points of intersection of the lines we solve for x and y using the equations we have

3x + 7y = 20...(1)

x - 7y = 4 ...(2)

(1) + (2)

=> 4x = 24

=> x= 24/4

=> x = 6

Substituting in (1)

3x + 7y = 20

=> 3*6 + 7y = 20

=> 7y = 20 - 18

=> 7y = 2

=> y = 2/7

**Therefore the point of intersection is ( 6, 2/7)**

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

3x+7y = 20 (1)

x-7y = 4 (2)

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

We'll solve the system using elimination method.

We'll add (1) + (2):

3x+7y+x-7y = 20+4

We'll eliminate and combine like terms:

4x = 24

We'll divide by 4:

**x = 6**

We'll substitute x in (2) and we'll get:

6-7y = 4

We'll subtract 6 both sides:

-7y = 4 - 6

-7y = -2

We'll divide by -7 both sides:

**y = 2/7**

**The solution of the system represents the coordinates of the intercepting point: (6 , 2/7).**