SOLUTION: Please help I'm stuck! State whether the system is consistent and independent, consistent and dependent or inconsistent. 2x - y = -7 x + y = 4

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Question 59972This question is from textbook Alegbra Concepts and Applications
: Please help I'm stuck!
State whether the system is consistent and independent, consistent and dependent or inconsistent.
2x - y = -7
x + y = 4This question is from textbook Alegbra Concepts and Applications

Answer by funmath(2873) About Me  (Show Source):
You can put this solution on YOUR website!

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!!!