Find the value of k for which the following system of equations has a unique solution:
Question:

Find the value of k for which the following system of equations has a unique solution:

$4 x+k y+8=0$

$2 x+2 y+2=0$

Solution:

GIVEN:

$4 x+k y+8=0$

$2 x+2 y+2=0$

To find: To determine to value of k for which the system has a unique solution.

We know that the system of equations

$a_{1} x+b_{1} y=c_{1}$

$a_{2} x+b_{2} y=c_{2}$

For unique solution

$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

Here,

$\frac{4}{2} \neq \frac{k}{2}$

$k \neq \frac{4 \times 2}{2}$

$k \neq 4$

Hence for $k \neq 4$ the system of equation has unique solution