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

2 x + 3 y - 6 = 0

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2 x + 2 y - 8 = 0

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2 x + y - 8 = 0

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2 x + 7 y - 8 = 0

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Solution

The correct option is A $2 x + 3 y - 6 = 0$
For the two lines to be parallel and giving no solutions,the condition of two lines,

$a_{1} x + b_{1} y = c_{1}$ and $a_{2} x + b_{2} y = c_{2}$ is

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

Thus for finding a parallel line against the equation $2 x + 3 y = 8$ ,we can take any line of the form $2 x + 3 y = n$ .where ‘n’ can take any real value except 8.

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Similar questions

Question 6 (iii)
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

Q. Given the linear equation

2 x + 3 y - 8 = 0

, write another linear equation in two variables such that the geometrical representation of the pair so formed is of intersecting lines.

Q. Given the linear equation

2 x + 3 y - 8 = 0,

write another linear equation in two variables such that geometrical representation of the pair so formed is
(i) intersecting lines
(ii) Parallel lines
(iii) coincident lines

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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 of parallel lines.

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