# Chapter 6 - Systems of Equations and Inequalities - 6-4 Application of Linear Systems - Practice and Problem-Solving Exercises - Page 387: 17

$A= -3$ $B= -2$

#### Work Step by Step

$Ax-2By =6$ and $3Ax-By = -12$ solution is (2,3) $A2-2B3 =6$ and $3A2-B3 = -12$ $2A-6B = 6$ and $6A-3B = -12$ $2A-6B = 6$ $6A-3B = -12$ $6A-3B = -12$ $-2*(6A-3B = -12)$ $-12A+6B =24$ $2A-6B = 6$ $-12A+6B =24$ $(2A-6B) + (-12A+6B) = (6+24)$ $-10A = 30$ $-10A/-10 = 30/-10$ $A = -3$ $2A -6B = 6$ $2*-3 -6B = 6$ $-6-6B = 6$ $-6-6B -6+6B = 6-6+6B$ $-12 = 6B$ $-12/6 = 6B/6$ $-2 = B$

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