Verify d1 and d2 are coincidental. d1:2x+3y-1=0; d2:4x+6y-2=0.
d1: 2x + 3y -1 = 0
d2= 4x + 6y -2 = 0
Let us factor 2 in d2:
d2: 2(2x + 3y -1) = 0
We notice that d2 = 2*d1
That means that d1 and d2 has the same coordinates.
Then d1 and d2 are coincidental.
First, we'll check if the equation is written in the general form, which is:
ax+by+c = 0
We'll notice that the lines d1 and d2 are written in the general form.
The condition of 2 lines to be coincidental is:
a1/a2 = b1/b2 = c1/c2
d1: a1x + b1y + c1
d2: a2x + b2y + c2
We'll identify a1, a2, b1, b2, c1, c2.
a1 = 2, a2 = 4
b1 = 3, b2 = 6
c1 = -1, c2 = -2
Now, we'll form the ratios to verify if they are equal:
2/4 = 3/6 = -1/-2
After dividing the first ratio by 2, the second ratio by 3 and the third ratio by -1, we'll get:
1/2 = 1/2 = 1/2
So, d1 and d2 are coincidental.
d1 = 2x+3y-1 and d2 : 4x+6y-2 = 0
We see that d1*2 = d2, as 2 *(2x+3y-1)= 0 and d2 are same.
Therefore all the points on d2 satisfy d2 or viceversa. So d1 and d2 are coincident.