Chapter 11 - Systems of Equations and Inequalities - 11.3 Systems of Linear Equations: Determinants - 11.3 Assess Your Understanding - Page 743: 51

$x=-5$

We know that for a matrix \[ \left[\begin{array}{rr} a & b \\ c &d \\ \end{array} \right] \] the determinant, $D=ad-bc.$ Hence, the determinant is $D=(x\cdot3)-(x\cdot4)\\ D=3x-4x\\ D=-x$ The determinant is $5$ therefore $5=-x\\ -5=x$