Question

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

Answer 1

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
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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
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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