Answer
$\left|\begin{array}{ll}{5}&{3}\\{-3}&{-4}\end{array}\right|$
Work Step by Step
Cramer's rule states that
$a x+b y=p \\ cx+dy=q$
$\triangle=\left|\begin{array}{ll}{a}&{b}\\{c}&{d}\end{array}\right|, \triangle_{1}=\left|\begin{array}{ll}{p}&{b}\\{q}&{d}\end{array}\right|, \triangle_{2}=\left|\begin{array}{ll}{a}&{p}\\{c}&{q}\end{array}\right|$; $ x=\dfrac{\triangle_1}{\triangle}; y=\dfrac{\triangle_2}{\triangle} (D\displaystyle \neq 0)$
We are given the system of equations:
$2x+3y=5 \\x-4y=-3$
So, we can write:
$\triangle=\left|\begin{array}{ll}{2}&{3}\\{1}&{-4}\end{array}\right|$ and $x=\dfrac{\triangle_1}{\triangle}=\left|\begin{array}{ll}{5}&{3}\\{-3}&{-4}\end{array}\right|$
So, our missing expression is:
$\left|\begin{array}{ll}{5}&{3}\\{-3}&{-4}\end{array}\right|$
