SOLUTION: Classify the following systems of equations as consistent, inconsistent, or dependent WITHOUT using graphing, substitution and elimination methods. 12. ( x � 3y = 5 ) (3x

Question 376683: Classify the following systems of equations as consistent, inconsistent, or dependent WITHOUT using graphing, substitution and elimination methods.
12.
( x � 3y = 5 )
(3x � 9y = 15)

13.
(4x + 3y = 7 )
(2x � y = 10)

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
12. The bottom equation is just a multiple of the top equation (multiplied by 3), and so the system is dependent (or it has infinitely many solutions, corresponding to the coordinates of any point on either line.) Note also that the determinant of the coefficient matrix is zero, so Cramer's method cannot be used.

13. The determinant of the coefficient matrix is -10 (not equal to zero!), and so the system has a unique ordered pair (x,y) as solution, hence the system is consistent & independent.
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