Which is the relative position of d1 and d2 if d1 : x - y + 1 = 0 and d2 : x + y - 3 = 0

Expert Answers
hala718 eNotes educator| Certified Educator

d1; x-y + 1 = 0

d2: x+ y -3 = 0

Now we need to see if d1 and d2 intersect at certain point which is the solution for both equations:

Let us add both equations:

==> 2x -2 = 0

==> 2x = 2

==> x = 1

Then x + y -3 = 0

==> y= 3 -x = 3-1 = 2

==> y = 2

Then both lines intersect at the point (1,2)

giorgiana1976 | Student

The relative position of d1 and d2 could be: concurrent, parallel or perpendicular.

Let's verify if d1 and d2 are intercepting each other. For this reason, we'll verify if the system formed by the equations of d1 and d2 has a solution, this solution representing the coordinates of the intercepting point of d1 and d2.

We'll form the system:

x - y + 1 = 0 

 x + y - 3 = 0

We'll re-write the system, moving the free terms to the right side, in each equation:

x - y = -1 (1)

x + y = 3 (2)

We'll solve the system using the elimination method.

We'll add (1)+(2) and we'll remove the like terms:

2x = 2

We'll divide by 2:

x = 1

We'll substitute x in the relation (1):

1 - y = -1

y = 1+1

y = 2

The system has the solution  (1,2), which is the intercepting point of d1 and d2, so d1 and d2 are concurrent.