Question

For which value of the given system of equations have infinitely many solution, $(k-3)x+3y=k$ and $kx+ky=12$

• A. $-6$
• B. $6$
• C. $0$
• D. $3$

Answer 1

The correct option is B $6$

Using conditions for consistency of equations,given system has infinitely many solutions if

$\frac{k-3}{k}=\frac{3}{k}=\frac{k}{12}$

$⟹3\times 12=k^2$

$⟹k=6$ or $k=-6$

Subtituting in $\frac{k-3}{k}=\frac{3}{k}$

we found that $k=6$ is solution