Question

Find the value of k if the following equation are consistent kx+3y+1=0......x+2y+1=0......x+y=0​

Answer 1

Given:

Equations $kx+3y+1=0$ , $x+2y+1=0$  and  $x+y=0​$ are consistent.

To Find:

Value of the k?

Solution:

Since, given equations $kx+3y+1=0$ , $x+2y+1=0$  and  $x+y=0​$ are consistent.

we treating the given system as , 3 equation in 3 variable.

therefore, Augmented metric is

$\left[\begin{array}{cccc}k&3&0&-1\\1&2&0&-1\\1&1&0&0\end{array}\right]$

above, system of equation is consistent if

$\left[\begin{array}{ccc}k&3&-1\\1&2&-1\\1&1&0\end{array}\right]=0$

⇒ $k(0+1)-3(0+1)-1(1-2)=0$

⇒ $k-3+1=0$

⇒ $k=2$

Hence, value of k is 2 for the given consistent system of equation.