MathematicsIf the system of equations 3x+y=1 and (2k-1)x+(k-1)y=2k+1 is inconsistent, then k= ?

If the system of equations $3 x + y = 1$ and $(2 k - 1) x + (k - 1) y = 2 k + 1$ is inconsistent, then $k =$ ?

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A
$1$
B
$- 1$
C
$- 2$
D
$2$

Solution:

The given pair of equations are

3 x + y = 1

and

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

.
The system of equations is inconsistent if

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

.
Here,

\frac{3}{2 k - 1} = \frac{1}{k - 1} \neq \frac{1}{2 k + 1}

⇒

3 k - 3 = 2 k - 1

⇒

k = 2

Hence, the correct option is 4.

If the system of equations $3 x + y = 1$ and $(2 k - 1) x + (k - 1) y = 2 k + 1$ is inconsistent, then $k =$ ?

Solution:

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