If a pair of linear equations is consistent,
Question:

If a pair of linear equations is consistent, then the lines will be

(a) parallel

(b) always coincident

(c) intersecting or coincident

(d) always intersecting

Solution:

(c) Condition for a consistent pair of linear equations

$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$ [intersecting lines having unique solution]

and    $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$ [coincident or dependent]

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