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How to find the values of c and d in the following equations:c+2d=6 -3c-6d=-18

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to eliminate one variable we can multiply times 3 the first equation and add to the second equation
3c+6d = 18
-3c - 3d=-18
The two equations are the same thing and the system is undetermined.
The determinant of the system is Zero so the system is undetermined. This is a so called inconsistent system.