State whether the given statement is true or false:
A pair of linear equations is given by $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ also $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ .
In this case, the pair of linear equations is consistent.

True

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False

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Solution

The correct option is A True
If $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ .
The lines are coincident and infinitely many solutions are obtained.
Therefore, in this case, the pair of linear equations is consistent.
The correct answer is True.

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