Question
If $\left|\begin{array}{ll}2 & 3 \\ y & x\end{array}\right|=3,\left|\begin{array}{ll}x & y \\ 4 & 2\end{array}\right|=5$ then find value of $x$ and $y$.
✓
Answer
Given : $\left|\begin{array}{ll}2 & 3 \\ y & x\end{array}\right|=3,\left|\begin{array}{ll}x & y \\ 4 & 2\end{array}\right|=5$
$
\begin{array}{l}
\therefore \quad \begin{array}{l}
2 x-3 y=3 .....(1) \\
2 x-4 y=5 .......(2)
\end{array}
\end{array}
$
Subtract equation (2) from equation (1)
$
y=-2
$
On putting the value of $y$ in equation (1)$
\begin{aligned}
& & 2 x-3 \times(-2) & =3 \\
\Rightarrow & & 2 x+6 & =3 \\
\Rightarrow & & x & =\frac{-3}{2}
\end{aligned}
$
$
\begin{array}{l}
\therefore \quad \begin{array}{l}
2 x-3 y=3 .....(1) \\
2 x-4 y=5 .......(2)
\end{array}
\end{array}
$
Subtract equation (2) from equation (1)
$
y=-2
$
On putting the value of $y$ in equation (1)$
\begin{aligned}
& & 2 x-3 \times(-2) & =3 \\
\Rightarrow & & 2 x+6 & =3 \\
\Rightarrow & & x & =\frac{-3}{2}
\end{aligned}
$
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