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# 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: (iii) coincident lines

Q6.    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:

(iii) coincident lines

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Given the equation,

$2x + 3y -8 =0$

As we know that the condition for the coincidence  of the lines  $a_1x+b_1y+c_1=0\:and\:a_2x+b_2y+c_2=0$, is,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

So any line with this condition can be  $4x+6y-16=0$

Here,

$\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2}$

$\frac{b_1}{b_2}=\frac{3}{6}=\frac{1}{2}$

$\frac{c_1}{c_2}=\frac{-8}{-16}=\frac{1}{2}$

As

$\frac{1}{2}=\frac{1}{2}=\frac{1}{2}$   the line satisfies the given condition.

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