Re: Can someone tell me what this system is considered to be
Hello, rachael724!
I am trying to solve a problem, but I don't know what this system is considered:
independent, inconsistent or dependent?
Evidently, you don't know the three types . . .
Independent: the system has a unique solution.
. . You
can solve it.
Inconsistent: the system has
no solution.
. . You arrive at a false statement, like: \(\displaystyle 2\,=\,3.\)
Dependent: the system has
too many solutions.
. . You arrive at a true statement, like: \(\displaystyle 0\,=\,0\)
.\(\displaystyle 2x\,-\,3y\:=\;6\)
\(\displaystyle 4x\,-\,6y\:=\,12\)
We will try to solve this system.
Multiply the first equation by -2:
.-\(\displaystyle 4x\,+\,6y\:=\,-12\)
. . . . .Add the second equation:
. \(\displaystyle 4x\,-\,6y\:=\;\,12\)
. . . . . . . . . . . . . . . .And we get:
. . . . . . . \(\displaystyle 0\,=\,0\)
This is a true statement (regardless of the value of \(\displaystyle x\) or \(\displaystyle y\)).
. . The system is
dependent.
