Question

Do tje equations 4x+3y-1=5 and 12x+9y=15 repesent a pair of coincident line?Justify your answer.

Answer 1

We know that, if any line is coincident to other then it should have a condition-

a1/a2=b1/b2=c1/c2

here, a1=4 b1=3 c1=-6

a2=12 b2=9 c2=-15

so, a1/a2=4/12=1/3

b1/b2=3/9=1/3

c1/c2=-6/-15=2/5

hence, a1/a2=b1/b2 but not equal to c1/c2 so this pair of lines are not coincident.

Hope! You will be able to understand my concept.

THANKS!