Without graphing, answer the questions for the following linear system.
y−x=−3
x+y=8
(a) is the system inconsistent, or are the equations dependent, or neither?
(b) is the graph a pair of intersecting lines, a pair of parallel lines, or one line?
(c) does the system have one solution, no solution, or an infinite number of solutions?

We don`t have to graph, but we can solve this system:
y - x = - 3
x + y = 8 ⇒ y = 8 - x

8 - x - x = - 3
- 2 x = - 11,  x = - 11 : ( - 2 ) = 5.5
y = 8 - 5.5 = 2.5
System is independent: lines meet in one point. There is only one solution.
Answers:
( a ) The system is neither inconsistent, nor dependent.
( b ) A pair of intersecting lines.
( c ) One solution.

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