Chapter 10 - Systems of Equations and Inequalities - Section 10.3 Systems of Linear Equations: Determinants - 10.3 Assess Your Understanding - Page 761: 51

$x=-5$

The determinant for a 2 by 2 matrix can be computed as: $Determinant (D)= \begin{vmatrix} A & B \\ C & D\end{vmatrix}=AD-BC$ Therefore, $Det=\begin{vmatrix} x & x \\ 4 & 3 \end{vmatrix}=3x-4x=-x$ Since $det=5$ So, $-x=5 \implies x=-5$