Find the value of $k$ for which the system
$kx+2y=5$

$3x+y=1$
has a unique solution.

Given: 

The given system of equations is:

$kx+2y=5$

$3x+y=1$

To do: 

We have to find the value of $k$ for which the given system of equations has a unique solution.

Solution:

The given system of equations can be written as:

$kx+2y-5=0$

$3x+y-1=0$

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 a unique solution is:

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

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

$a_1=k, b_1=2, c_1=-5$ and $a_2=3, b_2=1, c_2=-1$

Therefore,

$\frac{k}{3}≠\frac{2}{1}$

$k≠ 3\times2$

$k≠ 6$

The value of $k$ for which the given system of equations has a unique solution is $k≠ 6$.

Tutorialspoint

e

Updated on: 10-Oct-2022

26 Views

Kickstart Your Career

Get certified by completing the course

Get Started