Given the linear equation 2x + 3y - 8 = 0,wri | vedclass

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(A) For two linear equations $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to represent coincident lines,the condition is $\frac{a_1}{a_2} = \fr

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$4x + 6y - 16 = 0$

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(A) For two linear equations $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to represent coincident lines,the condition is $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$.Given the equation $2x + 3y - 8 = 0$,we have $a_1 = 2, b_1 = 3, c_1 = -8$.To find another equation,we can multiply the given equation by any non-zero constant $k$. Let $k = 2$.Multiplying the equation by $2$,we get $2(2x + 3y - 8) = 2(0)$,which simplifies to $4x + 6y - 16 = 0$.Checking the condition: $\frac{2}{4} = \frac{3}{6} = \frac{-8}{-16} = \frac{1}{2}$.Since the ratios are equal,the lines are coincident. Thus,$4x + 6y - 16 = 0$ is a valid answer.

Given the linear equation $2x + 3y - 8 = 0$,write another linear equation in two variables such that the geometrical representation of the pair so formed is coincident lines.

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