Question

Find the value of K for which the system of following equations has a unique solution 2x - y = 5 , Kx - 8y = 7

Answer 1

Step-by-step explanation:

Since, system of equations has a unique solution.

Therefore,

$\frac{2}{k} \neq \frac{1}{8} \\ \therefore \: k \times 1 \neq8 \times 2 \\ k \neq \: 16 \\ hence \: given \: system \: of \: linear \: \\ equations \: have \: uniqe \: solution \\ \: for \: all \: values \: of \:k \: except \: 16.$

Answer 2

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

Step-by-step explanation:

Given : Equations $2x-y = 5, Kx-8y = 7$

To find : The value of k for which the following system of equation has a unique solution.

Solution :  

When the system of equation is in form $a_1x+b_1y+c_1=0,\ a_2x+b_2y+c_2=0$ then the condition for a unique solutions is  

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

Comparing, $a_1=2,b_1=-1,c_1=-5,a_2=K,b_2=-8,c_1=-7$

Substituting the values,

$\frac{2}{K}\neq\frac{-1}{-8}$

$2\times -8=-1\times K$

$-K=-16$

$K=16$

Therefore, the value of k is 6 for which the system of following equations has a unique solution.

#Learn more

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