Question

Find the value of k for which the pair of linear equations kx-y=2 and 6/7x-2/3y=3 has a unique solution

Answer 1

we have to find the value of k for which the pair of equation kx - y = 2 and 6/7x - 2/3y = 3 has a unique solution.

condition, for unique solution in case of two pair of linear equations $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ is
$\frac{a_1}{a_2}\neq\frac{b_1}{b_2}$

so, $\frac{k}{\frac{6}{7}}\neq\frac{-1}{-\frac{2}{3}}$

$\frac{7k}{6}\neq\frac{3}{2}$

$k\neq\frac{9}{7}$

hence, $k\in R-\{\frac{9}{7}\}$
means value of K belongs to all real numbers except 9/7