Answer

2.1.) No Solutions, Inconsistent System

x + y = 5

-

x + y = 15

0 = - 10 (which is false)

2.) One Solution, Independent System

x + y = 5

-

x - 2y = 4

3y = 1

y = 1/3

x + 1/3 = 15/3

x = 14/3

3.) Infinitely many solutions, Dependent System

x + y = 5

-

3x - 3y = 15

-2x - 2y = -10

2x + 2y = 10

y = 5 - x (from x + y = 5, where y is isolated)

2x + 2(5 - x) = 10

2x + 10 - 2x = 10

10 = 10

x = 5 - y (from x + y = 5, where x is isolated)

2(5 - y) + 2y = 10

10 - 2y + 2y = 10

10 = 10

Either way, you will get 10 if you isolate x or y.

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