Show that each one of the following systems of equations is inconsistent. $4x – 2y = 3$; $6x

Home » Show that each one of the following systems of equations is inconsistent. ; .

Show that each one of the following systems of equations is inconsistent.
$4x - 2y = 3$ ;
$6x - 3y = 5$ .

Show that each one of the following systems of equations is inconsistent.
$4x - 2y = 3$ ;
$6x - 3y = 5$ .

Solution:

We need to prove: Set of given lines are inconsistent.
The given set of lines are : –
$\begin{array}{l} 4 x-2 y=3 \\ 6 x-3 y=5 \end{array}$
Now, converting the following equations in matrix form,
$\begin{array}{l} \mathrm{AX}=\mathrm{B} \\ \left(\begin{array}{ll} 4 & -2 \\ 6 & -3 \end{array}\right)\left(\begin{array}{l} x \\ y \end{array}\right)=\left(\begin{array}{l} 3 \\ 5 \end{array}\right) \\ 4 \mathrm{R}_{2}-6 \mathrm{R}_{1} \\ \left(\begin{array}{cc} 4 & -2 \\ 0 & 0 \end{array}\right)\left(\begin{array}{l} x \\ y \end{array}\right)=\left(\begin{array}{l} 3 \\ 2 \end{array}\right) \end{array}$
Again on converting into equation form, we obtain
$\begin{array}{l} 4 x-2 y=3 \\ 0 x+0 y=2 \end{array}$
$\therefore 0=2$
Which is not true
$\begin{array}{l} \therefore 4 \mathrm{x}-2 \mathrm{y}=3 \\ 6 \mathrm{x}-3 \mathrm{y}=5 \text { are inconsistent } \end{array}$