Question

if the given pair of linear equations kx+7y-6=0and 10x+14y-12=0has infinitely many solutions then find the value of k​

Answer 1

EXPLANATION.

=> Given pair of linear equation

=> kx + 7y - 6 = 0 ......(1)

=> 10x + 14y - 12 = 0 .....(2)

$\sf \to \: \dfrac{a_{1} }{a_{2} } = \dfrac{b_{1} }{b_{2}} = \dfrac{c_{1} }{c_{2}} \\ \\ \\ \sf \to \: \frac{k}{10} = \frac{7}{14} = \frac{ - 6}{ - 12} \\ \\ \\ \sf \to \: \frac{k}{10} = \frac{1}{2} = \frac{1}{2}$

=> case = 1.

$\sf \to \: \dfrac{k}{10} = \dfrac{1}{2} \\ \\ \sf \to \: 2k = 10 \\ \\ \sf \to \: k \: = 5$

=> case = 2.

$\sf \to \: \dfrac{k}{10} = \dfrac{1}{2} \\ \\ \sf \to \: 2k = 10 \\ \\ \sf \to \: k \: = 5$

Therefore,

Value of k = 5.