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.

2 x + 3 y + 9 = 0

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6 x + 9 y + 9 = 0

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3 x + 2 y + 9 = 0

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None of these

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Solution

The correct option is D $3 x + 2 y + 9 = 0$
Given equation is $2 x + 3 y - 8 = 0$
So any line which will satisfy the condition of intersecting the given line if,
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} . . . (1)$
Thus required line can be, $3 x + 2 y + 4 = 0$
Hence, the graph of the two equations will be two intersecting lines.

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2 x + 3 y - 8 = 0,

2 x + 3 y - 8 = 0

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