SOLUTION: hello how do i determine whether each system is independen, inconsisitend, or dependent: 2x + 2y = 8 x + y = 4 thank you!

Question 62281This question is from textbook
: hello
how do i determine whether each system is independen, inconsisitend, or dependent:
2x + 2y = 8
x + y = 4
thank you! This question is from textbook

Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
hello
how do i determine whether each system is independent, inconsisitent, or dependent:
E1: 2x + 2y = 8
E2: x + y = 4
If you try to eliminate the x's by multiplying E2 by -2 and adding E1+E2, both the x's and the y's are eliminated.
E2: -2(x+y)=-2(4)---> -2x-2y=-8
:
2x+2y=8
-2x-2y=-8
___________
0=0
This system is dependent because the variables were both eliminated and 0=0. That means that graphically they are the same line. There are infinitely many solutions because the lines have all points in common. Because there are solutions this is also consistent.
:
If we got 0= anything, but 0, it would be independent because they are separate lines. Graphically they would be parallel lines that never intersect. Because they never intersect there is no solution and therefore inconsistent.
:
If both our variables were not eliminated, they would be independent because they are different lines and consistent because there is exactly one solution.
Happy Calculating!!!
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