Find the value of $k$ for which the following system of equations has no solution:
$kx\ -\ 5y\ =\ 2$$6x\ +\ 2y\ =\ 7$

Given: 

The given system of equations is:

$kx\ -\ 5y\ =\ 2$

$6x\ +\ 2y\ =\ 7$

To do: 

We have to find the value of $k$ for which the given system of equations has no solution.

Solution:

The given system of equations can be written as:

$kx\ -\ 5y\ -\ 2=0$

$6x\ +\ 2y\ -\ 7=0$

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 has no solution 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,

$a_1=k, b_1=-5, c_1=-2$ and $a_2=6, b_2=2, c_2=-7$

Therefore,

$\frac{k}{6}=\frac{-5}{2}≠\frac{-2}{-7}$

$\frac{k}{6}=\frac{-5}{2}≠\frac{2}{7}$

$\frac{k}{6}=\frac{-5}{2}$

$k\times2=-5\times6$

$2k=-30$

$k=\frac{-30}{2}$

$k=-15$

The value of $k$ for which the given system of equations has no solution is $-15$. 

Tutorialspoint

e

Updated on: 10-Oct-2022

29 Views

Kickstart Your Career

Get certified by completing the course

Get Started