The value of c for which the pair of equation | vedclass

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(B) The condition for a pair of linear equations $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to have infinitely many solutions is $\frac{a_1}{

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no value

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(B) The condition for a pair of linear equations $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to have infinitely many solutions is $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$.The given equations are $cx - y - 2 = 0$ and $6x - 2y - 3 = 0$.Here,$a_1 = c, b_1 = -1, c_1 = -2$ and $a_2 = 6, b_2 = -2, c_2 = -3$.Applying the condition: $\frac{c}{6} = \frac{-1}{-2} = \frac{-2}{-3}$.This simplifies to $\frac{c}{6} = \frac{1}{2} = \frac{2}{3}$.Since $\frac{1}{2} 
eq \frac{2}{3}$,there is no value of $c$ that satisfies both equalities simultaneously.Therefore,the pair of equations will have no value of $c$ for which they have infinitely many solutions.

The value of $c$ for which the pair of equations $cx - y = 2$ and $6x - 2y = 3$ will have infinitely many solutions is

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