# For what value of k the following system of equations will be inconsistent?

Question:

For what value of k the following system of equations will be inconsistent?

$4 x+6 y=11$

$2 x+k y=7$

Solution:

GIVEN:

$4 x+6 y=11$

$2 x+k y=7$

To find: To determine for what value of k the system of equation will be inconsistent

We know that the system of equations

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

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

For the system of equation to be inconsistent

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

Here,

$\frac{4}{2}=\frac{6}{k} \neq \frac{11}{7}$

$\frac{4}{2}=\frac{6}{k}$

$k=\frac{12}{4}$

$k=3$

Hence for $k=3$ the system of equation will be inconsistent.