Question

The value of k for which the pair of linear equations kx+3y+(3-k)=0 and 12x+ky-k=0 have infinitely Many solutions is ​

Answer 1

Answer:-

• kx+3y+(3-k)=0---(1)
• 12x+ky-k=0-----(2)

If it has infinite solutions then

$\boxed{\sf \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}}$

$\\ \sf\longmapsto \dfrac{k}{12}=\dfrac{3}{k}=\dfrac{3-k}{-k}$

$\\ \sf\longmapsto \dfrac{k}{12}=\dfrac{3}{k}$

$\\ \sf\longmapsto k^2=36$

$\\ \sf\longmapsto k=\sqrt{36}$

$\\ \sf\longmapsto k=6$