Chapter 11 - Systems of Equations and Inequalities - 11.3 Systems of Linear Equations: Determinants - 11.3 Assess Your Understanding - Page 742: 10

$-2$

We know that for a matrix \[ \left[\begin{array}{rr} a & b \\ c &d \\ \end{array} \right] \] the determinant is $D=ad-bc.$ Hence, here we have $D=(-4\cdot3)-[2\cdot(-5)]\\ D=-12-(-10)\\ D=-12+10\\ D=-2$