Question

For what values of k following pairs of linear equations have no solutions 3x + 2y = 1
(3k - 1) X + (2k - 1) y = 2k + 1

Answer 1

Answer:

The given system of equations always have solution for any real values of k

Step-by-step explanation:

Concept used:

If the equations

$a_1x+b_1y=c_1$

$a_2x+b_2y=c_2$ have solution, then $a_1b_2-a_2b_1\neq0$

Given equations are

$3x + 2y=1$

$(3k - 1) x + (2k - 1) y = 2k + 1$

Now

$a_1b_2-a_2b_1$

$=3(2k-1)-(3k-1)2$

$=6k-3-6k+2$

$=-1\neq0$

Therefore the given system of equations has solution for any real values of k