The equation $3 x - 5 y + 2 = 0$ and $6 x + 4 = 10 y$ have

no solution

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a single solution

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two solutions

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an infinite number of solutions

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Solution

The correct option is D an infinite number of solutions
The given equations are
$3 x - 5 y + 2 = 0$ ,
$6 x + 4 = 10 y \Rightarrow 6 x - 10 y + 4 = 0$
Comparing with general form of equations, we get
$a_{1} = 3, b_{1} = - 5, c_{1} = 2$ and $a_{2} = 6, b_{2} = - 10, c_{2} = 4$
$\frac{3}{6} = \frac{- 5}{- 10} = \frac{2}{4} = \frac{1}{2}$
Hence, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$
So, the given equations have infinite number of solutions.

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