Question

If the pair linear equations x + 3y = 1 and 2x + 6y = K are coincident with each other, the value of 'K' is A] 2 B] –2 C] 3 D] –3

Answer 1

Answer:

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

If the pair linear equations x + 3y = 1 and 2x + 6y = K are coincident with each other, the value of 'K' is

A] 2

B] –2

C] 3

D] - 3

CONCEPT TO BE IMPLEMENTED

For the given two linear equations

$\displaystyle \sf{ a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0}$

Consistent :

One of the Below two condition is satisfied

1. Unique solution :

$\displaystyle \sf{ \: \frac{a_1}{a_2} \ne \frac{b_1}{b_2} }$

2. Infinite number of solutions : ( Coincident lines )

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} = \: \frac{c_1}{c_2}}$

Inconsistent :

NO solution

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \: \frac{c_1}{c_2}}$

EVALUATION

Here the given system of equations are

x + 3y = 1 and 2x + 6y = K

Now the pair linear equations are coincident with each other

Thus we get

$\displaystyle\sf{ \frac{1}{2} = \frac{3}{6} = \frac{1}{K} }$

$\displaystyle\sf{ \implies \: \frac{1}{2} = \frac{1}{K} }$

$\displaystyle\sf{ \implies \: {K} = 2 }$

FINAL ANSWER

Hence the correct option is A] 2

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