What is the intercepting point of the lines 3x + 7y = 20 ; x - 7y = 4 .

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).