Verify if the line x=42-14y intersects the line y=2x-11.

To determine if the lines are intercepting each other,
we'll have to solve the system formed form the equations of the lines and to see if it
has a solution. The solution of the system represents the intercepting point of the
lines.

We'll change the 1st equation
in:

 x+14y=42 (1)

We'll change
the 2nd equation in:

2x-y=11 
(2)

We'll solve the system using elimination method. For
this reason, we'll multiply (2) by 14:

28x - 14y = 154
(3)

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

28x
- 14y +  x + 14y = 154 + 42

We'll eliminate like
terms:

29x = 196

We'll divide
by 29:

x = 196/29

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

196/29 +
14y=42

We'll subtract 196/29 both
sides:

14y = 42 - 196/29

14y =
(1218-196)/29

We'll divide by
14:

y =
1022/406

The lines are intercepting and the
coordinates of the intercepting point are: (196/29,
1022/406).