Question

the value of k for which the system equation x+3y-4=0 and 2x+ky=7 is in consistent is. Pleezzzz help....... ​

Answer 1

Answer:

k ∈ R - {6}

Step-by-step explanation:

System of linear equations is consistent if it has at least one solution.

System of linear equations is consistent independent if it has only one solution.

System of linear equations is consistent dependent if it has infinitely many solutions.

x + 3y - 4 = 0 ( $a_{1}$ = 1, $b_{1}$ = 3, $c_{1}$ = - 4 )

2x + ky - 7 = 0 ( $a_{2}$ = 2, $b_{2}$ = k, $c_{2}$ = - 7 )

$a_{1}$ / $a_{2}$ ≠ $c_{1}$ / $c_{2}$ , thus the system has to be consistent independent and condition for this is $a_{1}$ / $a_{2}$ ≠ $b_{1}$ / $b_{2}$

Let find value of "k" when  $a_{1}$ / $a_{2}$ ≠ $b_{1}$ / $b_{2}$

$\frac{1}{2}$ ≠ $\frac{3}{k}$ ===> k ≠ 6

So, the given system of equation is consistent for any real numbers excluding 6, or mathematically k ∈ R - {6}