SOLUTION: I have a problem can you help me Its about solving for the value of k that makes each of the following an inconsistent system 1. y=kx-3 3x+3y=6 2. y=kx-2 3x-y=8

Hi  

A consistent system has at least one solution.

An inconsistent system has no solutions.

An independent system has exactly one solution.

A dependent system has infinitely many solutions.



the value of k that makes each of the following an inconsistent system (no solutions)

Parallel Lines have no solution in common 

Parallel Lines have same slope  

  

1. 

( same as 3x + 3y = 6)

Therefore IF (parallel lines, therefore, no solutions)

2. y=kx-2

   y= 3x -8   same as 3x-y=8 

 (parallel lines, therefore, no solutions)



3. y = (3/2)x - 7/2  same as 3x-2y=7

   y=  kx-5 

 (parallel lines, therefore, no solutions)



k that makes each of the following a dependent system(infinitely many solutions

Same Lines have infinitely many solutions

Same lines can be just multiples of one another

4. x  -  ky = 4

0r 2x - 2ky = 8

   2x + 4y = 8

-2k = 4

  same line, infinitely many solutions

5. y = x/2 -3

   y = x/2 + k/2  same as 2y=x+k 

k/2 = -3

  same line, infinitely many solutions

consistent independent system (exactly one solution) 

Lines intersect

3. 3x+3y=-6 This a traditional line

3x - 2k = 6  0r  This represents a perpendicular line

ANY value of k would result in the two lines intersecting 



Wish You the Best in your Studies.