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