Calculate the intercepting point of the lines x+7y=21 and 2x-y=11

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

 x+7y=21 (1)

2x-y=11 
(2)

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

We'll solve the system using
elimination method. For this reason, we'll multiply (2) by
7:

14x - 7y = 77 (3)

We'll add
(3) to (1):

14x - 7y +  x+7y = 77 +
21

We'll eliminate like
terms:

15x = 98

We'll divide
by 15:

x =
98/15

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

98/15 + 7y=21

We'll
subtract 98/15 both sides:

7y = 21 -
98/15

7y = (21*15-98)/15

We'll
divide by 7:

y =
217/105

The coordinates of the
intercepting point are: (98/15 , 217/105).