Question

Find k if 3x+y=1 and (2k-1)x +(k-1)y=2k+1 has no solution

Answer 1

hope it helps u dear
Given system of equations is: 

3x+y=1 and

(2k-1)x+(k-1)y=2k+1

They can be rewrite as:

3x + y - 1 = 0 and

(2k-1)x + (k-1)y - (2k+1) = 0 

 

 We know that, for the given system to have no solution,=≠

⇒  

⇒ 3k - 3 = 2k - 1

⇒ k = 3-1

⇒ k = 2

Hence, for k = 2, the given system of equation will have no solution.

Answer 2

Hey there !!

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Given equations,
3x + y = 1
and
(2k–1)x + (k–1)y = 2k+1

Condition for no solution,
a1/a2 = b1/b2 ≠ c1/c2

Now, 3/(2k–1) = 1/(k–1) ≠ 1/(2k+1)
=> 3 / (2k–1) = 1 / (k–1)
=> 3(k–1) = (2k–1)
=> 3k–3 = 2k–1
=> 3k–2k = 3–1
=> k = 2

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