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
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.
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..
≠ ≠ ______ (1)
Here..
- = k
• = 3
- = 2
• = 1
- = 5
• = 1
Put the given values in (eq 1)
=> ≠
Cross-multiply them
=> k ≠ 3 × 2
=> k ≠ 6
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≠
_________
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✡ More information :
• For unique solutions
≠ ≠
• For infinity many solutions
= =
• For no solutions
= ≠
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