LuLuBirdy
Answered

Classify the system as independent, dependent, or inconsistent.


1: 4x+8y=12 (1 point)

x+2y=-3


2: y=2x-1 (1 point)

y=-2x+5


3: x-3y=2 (1point)

4x-12y=8

Verified Answer :

texaschic101
  1. 4x + 8y = 12....divide by 4
         x + 2y = 3
         2y = -x + 3
         y = -1/2x + 3/2...slope is -1/2, y int is 3/2
     
         x + 2y = -3
         2y = -x - 3
         y = -1/2x - 3/2...slope is -1/2 and y int is -3/2

    when the slopes are the same, and the y int are different, then the lines are parallel and never intersect...so they have no solution and are inconsistent
    =================
    2. y = 2x - 1...slope is 2 and y int is -1
        y = -2x + 5 ...slope is -2 and y int is 5
    when the slopes are different and the y int are different, then there is 1 solution making it independent
    =================
    3. 4x - 12y = 8...divide by 4
         x - 3y = 2
    same as other equation meaning the equations are the same line...meaning they have infinite solutions making them dependent

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