Question

Find the values of m for which the system of equations 5x-my=7 3x+7y= 5 will

have a unique solution​

Answer 1

$\textbf{Given:}$

$\textsf{Equations are}$

$\mathsf{5x-my=7,\;\;3x+7y=5}$

$\textbf{To find:}$

$\textsf{The values of m for which the system of the equations}$

$\textsf{will have unique solution}$

$\textbf{Solution:}$

$\underline{\textsf{Concept:}}$

$\mathsf{If\;the\;equations\;a_1\,x+b_1\,y=c_1,\;\;a_2\,x+b_2\,y=c_2\;have\;solution,}$

$\mathsf{then\;a_1\,b_2-a_2\,b_1{\neq}0}$

$\mathsf{For\;unique\;solution,}$

$\mathsf{a_1\,b_2-a_2\,b_1{\neq}0}$

$\mathsf{5(7)-3(-m){\neq}0}$

$\mathsf{35+3m{\neq}0}$

$\mathsf{3m{\neq}-35}$

$\implies\boxed{\mathsf{m{\neq}\dfrac{-35}{3}}}$