Question

Find the value of k for which the following system of equations has a unique solution:
4x-5y=k2x-3y=12

Answer 1

Answer:

The given system of equation will have unique solution for all real values of k .

Step-by-step explanation:

Given as :

The two linear equation are

4 x - 5 y = k                      ........1

And

2 x - 3 y = 12                   ........2

For the system of equation have unique solution

$a_1$ x + $b_1$ y + $c_1$ = 0

$a_2$ x + $b_2$ y + $c_2$ = 0

$\dfrac{a_1}{a_2}$  $\neq$  $\dfrac{b_1}{b_2}$

while comparing the condition with give equation

i.e  $\dfrac{4}{2}$  $\neq$  $\dfrac{-5}{-3}$

So, k can have any real values

∴ The given system will have unique solution for all real values of k

Hence, The given system of equation will have unique solution for all real values of k . Answer