Question

If a1x+b1y+c1=0 and a2x+b2y+c2=0 lines are inconsistent lines, then the ratio of their coefficients is
a) a1/a2≠b1/b2
b) a1/a2=b1/b2≠c1/c2
c) a1/a2=b1/b2= c1/c2
d) a1/a2=b1/b2​

Answer 1

Answer:

(b) a1/a2 = b1/b2 # c1/c2

because these pair has parallel lines which does not has any solution.

Answer 2

Answer:

Given a pair of linear equations:

The two lines have a solution when.

For example, the following pair will have exactly one solution:

Let us calculate the ratio of :

Here, the ratio is not equal:

Hence, the pair of linear equation is consistent with exactly one solution.

If the ratio of  (equal), it will have consistent solution with infinite solutions.

Actually, the lines are identical.

For example:

Here,

So, the pair of linear equations is consistent with infinite solutions.

That means, the ratio of  are same but not equal to ratio . In this case, the lines will be parallel to each other and there will no or the pair of linear equation is inconsistent.

For example:

Here, the ratio is:

Hence, correct answer is option

Step-by-step explanation: