Question

For what value of k will the following equation has no solutions?<br />
3x + y = 1<br />
(2k - 1)x + (k - 1)y = 2k+1

Answer 1

hey dear friend

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,
=a1/a2=b1/b2#c1/c2
= 3/2k-1=1/k-1
⇒ 3k - 3 = 2k - 1
⇒ k = 3-1
⇒ k = 2
Hence, for k = 2, the given system of equation will have no solution.

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