Consistent Pair of Linear Equations

Video Explanation

Question

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

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

Solution

Step 1: Meaning of Consistent System

A system is said to be consistent if it has at least one solution.

Step 2: Possible Cases

A pair of linear equations can be:

• Intersecting lines → one solution
• Coincident lines → infinitely many solutions

Step 3: Conclusion

Since a consistent system has at least one solution, the lines must be:

✔ Intersecting (one solution) ✔ Coincident (infinite solutions)

Final Answer

\[ \text{The lines are intersecting or coincident.} \]