Chapter 11 - Systems of Equations and Inequalities - 11.3 Systems of Linear Equations: Determinants - 11.3 Assess Your Understanding - Page 743: 53

$x=\frac{13}{11}.$

We know that for a matrix \[ \left[\begin{array}{rrr} a & b & c \\ d &e & f \\ g &h & i \\ \end{array} \right] \] the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$ Hence here $D=x(3\cdot5-2\cdot2)-1(4\cdot5-2\cdot(-1))+1(4\cdot2-3\cdot(-1))=2\\x(11)-1(22)+1(11)=2\\11x-22+11=2\\11x=13\\x=\frac{13}{11}.$