Chapter 11 - Systems of Equations and Inequalities - 11.3 Systems of Linear Equations: Determinants - 11.3 Assess Your Understanding - Page 741: 4

False

If $D=0$ we have two possibilities: 1) $D_x=0,D_y=0,D_z=0$ 2) At least one of the determinants $D_x,D_y,D_z$ is not zero In the first case the system is consistent and dependent (thus it has infinitely many solutions). In the second case the system is inconsistent. Therefore the statement is FALSE.