Math, asked by athulkrishna50, 11 months ago

The pair of linear equations kx+2y=5 and 3x+y = 1 has a unique solution. (a) K=6 (b) k not equal to 6 (c) k=0 (d) k has any value

Answers

Answered by CaptainBrainly
93

Answer : Option [ b ] - k ≠ 6

SOLUTION :

Given,

Pair of linear equations :

kx+2y=5 and 3x + y = 1

If the equations have a unique solution then,

a1/a2 ≠ b1/b2 ≠ c1/c2

From above equations,

a1 = k b1 = 2 c1 = 5

a2 = 3 b2 = 1 c2 = 1

k/3 ≠ 2/1

k × 1 ≠ 3 × 2

k ≠ 6

Therefore, the value of k ≠ 6.

Answered by Anonymous
81

kx + 2y = 5

3x + y = 1

_______________ [GIVEN]

• We have to find the value of of k if the pair of linear equations has unique solution.

_______________________________

For unique solutions..

\dfrac{a_{1}}{a_{2}}\dfrac{b_{1}}{b_{2}}\dfrac{c_{1}}{c_{2}} ______ (1)

Here..

  • a_{1} = k

a_{2} = 3

  • b_{1} = 2

b_{2} = 1

  • c_{1} = 5

c_{2} = 1

Put the given values in (eq 1)

=> \dfrac{k}{3}\dfrac{2}{1}

Cross-multiply them

=> k ≠ 3 × 2

=> k ≠ 6

_____________________________

\bold{k}\bold{6}

_________ \bold{[ANSWER]}

_____________________________

✡ More information :

• For unique solutions

\frac{a_{1}}{a_{2}}\frac{b_{1}}{b_{2}}\frac{c_{1}}{c_{2}}

• For infinity many solutions

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}

• For no solutions

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}\frac{c_{1}}{c_{2}}

_______________________________

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