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Inconsistent pair of LE

If the two li...

Question

If the two lines are parallel and do not intersect, then the system of equations is ____.

A

inconsistent with one solution

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B

consistent with one solution

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C

consistent with many solutions

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D

inconsistent with no solution

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Solution

The correct option is D inconsistent with no solution
Detailed step-by-step solution:

We know that the system of equations is said to be consistent if it has at least one solution.
On the contrary, if the system of equations has no solution, then it is said to be inconsistent.

Parallel lines are lines that never meet each other.

Since the parallel lines do not intersect, there is no single point that will satisfy the system of equations. There exists no solution, thus the system of equations will be inconsistent with no solutions.

$\Rightarrow$ Option C is correct.

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Similar questions

Q. Which of the following statements are true and which are false?
(i) Two lines are parallel if they do not meet, even when produced.
(ii) Two parallel lines are everywhere the same distance apart.
(iii) If two line segments do not intersect, they are parallel.
(iv) If two rays do not intersect, they are parallel.

Q. If a pair of linear equations in two variables is consistent, then the lines represented by two equations are

(a) intersecting
(b) parallel
(c) always coincident
(d) intersecting or coincident

Q. State which of the following statements are true (T) or which are false (F):

(i) If two lines in the same plane do not interest, then they much be parallel.
(ii) Distance between two parallel lines is not same every where.
(iii) If m ⊥ i, n ⊥ i and m ≠ n, then m ∥ n.
(iv) Two non-intersection coplanar rays are parallel.
(v) If ray AB ∥ line , then line segment AB ∥ m.
(vi) If line AB ∥ line , then line segment AB ∥ m.
(vii) No two parallel segments intersect.
(viii) Every pair of lines is a pair of coplanar lines.
(ix) Two lines perpendicular to the same line are parallel.
(x) A line perpendicular to one of two parallel lines is perpendicular to the other.

Q. Read the following statements which are taken as axioms :
(i) If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.
(ii) If a transversal intersect two parallel lines, then alternate interior angles are equal.
Is this system of axioms consistent?

Q. If two lines do not intersect when extended infinitely, lines are called parallel lines.

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Inconsistent pair of LE

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