For what value of $k$ the following system of equations will be inconsistent?
$4x+6y=11$

$2x+ky=7$

Given: 

The given system of equations is:

$4x+6y=11$

$2x+ky=7$

To do: 

We have to find the value of $k$ for which the given system of equations will be inconsistent.

Solution:

The given system of equations can be written as:

$4x+6y-11=0$

$2x+ky-7=0$

The standard form of system of equations of two variables is $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y-c_{2}=0$.

The condition for which the above system of equations is inconsistent is:

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

Comparing the given system of equations with the standard form of equations, we have,

$a_1=4, b_1=6, c_1=-11$ and $a_2=2, b_2=k, c_2=-7$

Therefore,

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

$2=\frac{6}{k}≠\frac{11}{7}$

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

$2\times k=6$

$2k=6$

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

$k=3$

The value of $k$ for which the given system of equations is inconsistent is $3$. 

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Updated on: 10-Oct-2022

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