Question 59972

State whether the system is consistent and independent, consistent and dependent or inconsistent.

E1: 2x - y = -7

E2:  x + y = 4
If the system is solvable then it is consistent and independent.  If you add these two equations together only the y is eliminated so this is solvable, consistent and independent.  Graphically the lines intersect at one point and tehrefore the system has one solution.
:
If you go to eliminate one variable and both are eliminated, then there is one of two options, either you get 0=0 which is consistent and dependent.  Graphically they are the same line and share all points. (infinite solutions).  Or you get two numbers that aren't = like 1=-1, which is inconsitent.  Graphically, they are parallel lines that will never intersect. (no solution).
Happy Calculating!!!