Verify if the lines x-3y-2=0 and 2x+y-5=0 are intersecting .

To verify if the lines are intercepting, we'll have to
solve the system fomed by the equations of the lines. If the system has solution, this
solution represents the intercepting point of the
lines.

We'll re-write the equation, moving the number to
the right side:

x - 3y = 2
(1)

2x + y = 5 (2)

We'll
multiply (2) by 3:

6x + 3y = 15
(3)

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

x -
3y + 6x + 3y = 2 + 15

We'll combine and eliminate like
terms:

7x = 17

x =
17/7

We'll substitute x in
(1):

17/7 - 3y = 2

We'll
subtract 17/7 both sides:

-3y = 2 -
17/7

-3y = (14-17)/7

-3y =
-3/7

We'll divide by -3:

y =
1/7

The lines are intercepting and the
intercepting point is (17/7 ; 1/7).