Solve the following pairs of liner equation by the method of substitution:
$2 x + 3 y = 5, 2 x + 3 y = 7$

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Solution

We know that, for a pair of linear equation:
$a_{1} x + b_{1} x + c_{1} = 0$
$a_{2} x + b_{2} x + c_{2} = 0$
Has no solution if
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
Here:- $2 x - 3 y = 5$
$2 x = 3 y = 7$
$\frac{a_{1}}{a_{2}} = \frac{2}{2} = \frac{1}{1}; \frac{b_{1}}{b_{2}} = \frac{3}{3}; \frac{c_{1}}{c_{2}} = \frac{5}{7}$
Since $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$ , so given equation has no solution.

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