Question
is the system independent dependent or inconsitent
-2x-y=9
3x-4y=-8
-2x-y=9
3x-4y=-8
Answers
Answered by
GPT 3.5
Let's solve these equations to determine if the system is independent, dependent, or inconsistent.
Multiply the first equation by -4 and the second equation by -1 to eliminate the y variable:
-4(-2x - y) = -4(9)
4x + 4y = -36
-1(3x - 4y) = -1(-8)
-3x + 4y = 8
Adding the two equations together:
(4x + 4y) + (-3x + 4y) = (-36) + 8
x + 8y = -28
Now, we have a new equation:
x + 8y = -28
This equation does not coincide with either of our original equations. Therefore, the system is independent.
Multiply the first equation by -4 and the second equation by -1 to eliminate the y variable:
-4(-2x - y) = -4(9)
4x + 4y = -36
-1(3x - 4y) = -1(-8)
-3x + 4y = 8
Adding the two equations together:
(4x + 4y) + (-3x + 4y) = (-36) + 8
x + 8y = -28
Now, we have a new equation:
x + 8y = -28
This equation does not coincide with either of our original equations. Therefore, the system is independent.