#### Need solution for RD Sharma maths class 12 chapter Solution of Simultaneous Linear Equation exercise 7.1 question 4 subquestion (iii)

Inconsistent

Given:

$4x-2y=3 \quad , \quad 6x-3y=5$

Hint:

Inconsistent means two or more equations that are impossible to solve based on using one set of values for variables.

Solution:

The given system of equations can be expressed as follows

$A X=B \\ Here, \\ A=\left[\begin{array}{ll}4 & -2 \\ 6 & -3\end{array}\right] \quad, \quad X=\left[\begin{array}{c}x \\ y\end{array}\right] \quad and \quad B=\left[\begin{array}{l}3 \\ 5\end{array}\right] \\ Now, \\ |A|=\left|\begin{array}{ll}4 & -2 \\ 6 & -3\end{array}\right|=|-12+12|=0$

$C_{i j}\; be\; the\; co-\! f\! actor\; o\! f\; the\; elements\; a_{i j}\; in \; A=\left[a_{i j}\right].\; Then,$

\begin{aligned} &C_{11}=-1^{1+1}(-3)=-3 \quad, \quad C_{12}=-1^{1+2}(6)=-6 \\ &C_{21}=-1^{2+1}(-2)=2 \quad, \quad C_{22}=-1^{2+2}(4)=4 \\ &(\text { adjA }) B=\left[\begin{array}{ll} -3 & 2 \\ -6 & 4 \end{array}\right]\left[\begin{array}{l} 3 \\ 5 \end{array}\right]=\left[\begin{array}{c} -9+10 \\ -18+20 \end{array}\right]=\left[\begin{array}{l} 1 \\ 2 \end{array}\right] \neq 0 \end{aligned}

Hence, the given system of equation is inconsistent.