Question 1

What is a pair of linear equations in two variables?

Accepted Answer

A pair of linear equations in two variables consists of two equations of the form a1x + b1y + c1 = 0 and
a2x + b2y + c2 = 0, where x and y are unknowns.

Question 2

How many solutions can a pair of linear equations have?

Accepted Answer

The system can have one solution (if the lines intersect), no solution (if the lines are parallel), or infinitely many solutions (if the lines are coincident).

Question 3

What are the different methods to solve a pair of linear equations?

Accepted Answer

The common methods are the graphical method, substitution method, elimination method, and cross-multiplication method.

Question 4

What is the graphical method of solving linear equations?

Accepted Answer

The graphical method involves plotting both equations as straight lines on a coordinate plane. The point where the lines intersect is the solution.

Question 5

What does the consistency of a system of equations mean?

Accepted Answer

Consistency refers to whether the system has solutions. If the system has a unique or infinite number of solutions, it is consistent; if it has no solution, it is inconsistent.

Pair of Linear Equations in Two Variables Class-10th Board

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