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Find those values of $m$ the system of equation $2x+my-4=0;\ 3x-7y-10=0$, For which there is unique solution.
Given: Equations: $2x+my-4=0$; $3x-7y-10=0$$.
To do: To find the value of $m$ for the unique solution.
Solution:
Given equations are: $2x+my-4=0$; $3x-7y-10=0$.
For unique solution.
$\Rightarrow \frac{a_1}{a_2}≠\frac{b_1}{b_2}$
$\Rightarrow \frac{2}{3}≠\frac{m}{-7}$
$\Rightarrow 3m≠-7\times2$
$\Rightarrow m≠-\frac{14}{3}$
Thus, for $m≠-\frac{14}{3}$, there is a unique solution.
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