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The pair of linear equations $x + 2 y = 5, 3 x + 12 y = 10$ has ____ solution.

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Detailed Solution

The pair of linear equations

x + 2 y = 5, 3 x + 12 y = 10

has unique solution.
As general form of equation,

ax + by + c = 0

Given equations are:

x + 2 y = 5

3 x + 12 y = 10

From the equations we have:

\Rightarrow a_{1} = 1, b_{1} = 2

\Rightarrow a_{2} = 3, b_{2} = 12

If the equations are in the form of,

\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}

then the equations have unique solution.
So,

\frac{a_{1}}{a_{2}} = \frac{1}{3}

\frac{b_{1}}{b_{2}} = \frac{2}{12} = \frac{1}{6}

\Rightarrow \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}

.
Hence, the system of equations has a unique solution.

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