One equation of a pair of dependent linear eq | vedclass

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Question

(C) For a pair of linear equations to be dependent,they must represent the same line,meaning their coefficients must be proportional: $\frac{a_1}{a_2}

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$10x - 14y = -4$

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(C) For a pair of linear equations to be dependent,they must represent the same line,meaning their coefficients must be proportional: $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} = k$.Given equation: $-5x + 7y - 2 = 0$.Comparing with $a_1x + b_1y + c_1 = 0$,we have $a_1 = -5, b_1 = 7, c_1 = -2$.For the second equation,we multiply the given equation by a constant $k$. Let $k = 2$:$2(-5x + 7y - 2) = 2(0)$$-10x + 14y - 4 = 0$Rearranging this,we get $10x - 14y + 4 = 0$.Comparing this with option $(C)$: $10x - 14y = -4$ is equivalent to $10x - 14y + 4 = 0$.

One equation of a pair of dependent linear equations is $-5x + 7y = 2$. The second equation can be

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