Question

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

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Answer 1

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.

Answer 2

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.

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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

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$\bold{k}$ ≠ $\bold{6}$

_________ $\bold{[ANSWER]}$

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✡ 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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