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 0rThis represents a perpendicular line
ANY value of k would result in the two lines intersecting
Wish You the Best in your Studies.