State the condition for one solution, infinite solutions and no solution for a pair of linear equations.

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Solution

We have two linear equations
$a_{1} x + b_{1} y + c_{1} = 0 - - - - - - - - - - (1)$
$a_{2} x + b_{2} y + c_{2} = 0 - - - - - - - - - - (2)$

Condition for exactly one solution= $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

Condition for infinite solutions = $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

Condition for no solution = $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

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