Check whether the pair of equations $x + 3 y = 6$ , and $2 x - 3 y = 12$ is consistent. If so, solve graphically

Yes;

x = 6, y = 0

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No;

x = 6, y = 0

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Ambiguous

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Data insufficient

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Solution

The correct option is C Yes; $x = 6, y = 0$
The given pair can be written as
$x + 3 y - 6 = 0$ and $2 x - 3 y - 12 = 0$
Here $a_{1} = 1, b 1 = 3, c_{1} = - 6........... e q 1 a n d a_{2} = 2, b_{2} = - 3, c_{2} = - 12......... e q 2$
$∴ \frac{a_{1}}{a_{2}} = \frac{1}{2}, \frac{b_{1}}{b_{2}} = \frac{3}{- 6} = \frac{1}{- 2}$
Hence $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
Thus the given pair of equation is consistent.
To solve them graphically we have
Consider $x + 3 y - 6 = 0$
$x = 0 ⟹ y = 2$
$x = 3 ⟹ y = 1$
Join the points by drawing line.
Consider $2 x - 3 y - 12 = 0$
$x = 0 ⟹ y = - 4$
$x = 3 ⟹ y = - 2$
Join the two points by drawing line.
The given pair of linear equation has unique solution $x = 6$ and $y = 0$ .

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