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The equations $3 x + 17 y = 3, 7 x + 3 y = 7$ represent a pair of which type of lines?

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Coincident lines

Parallel lines

Intersecting lines

None of these

answer is C.

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Detailed Solution

Given pair of linear equations are,

3 x + 17 y = 3, 7 x + 3 y = 7

We know that the general form of linear equations is,

m 1 x + n 1 y + l = 0, m 2 x + n 2 y + l = 0

where

m 1, n 1, l 1, m 2, n 2, l 2

are all real numbers and

m 1 2 + n 1 2 ≠ 0, m 2 2 + n 2 2 ≠ 0

.
On comparing the given pair of linear equations with the general form we get,

m_{1} = 3, n_{1} = \frac{1}{7}, l_{1} = - 3

m_{2} = 7, n_{2} = 3, l_{2} = - 7

Then,

\Rightarrow \frac{m_{1}}{m_{2}} = \frac{3}{7}

\Rightarrow \frac{n_{1}}{n_{2}} = \frac{\frac{1}{7}}{3} = \frac{1}{21}

\Rightarrow \frac{l_{1}}{l_{2}} = \frac{- 3}{- 7} = \frac{3}{7}

From above,

\frac{m_{1}}{m_{2}} \neq \frac{n_{1}}{n_{2}}

So, the given pair of equations represents a pair of intersecting lines.
Hence, the correct option is 3.

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