Question

For these questions, state whether each system is consistent and independent, consistent and dependent, or inconsistent.
1. –x + y = –4
3x – 3y = 12

2. 2x – 5y = 8
15y – 6x = –24

Answer 1

1. y=x-4 if you solve by substitution
2. y=5/2y+4 if you solve by substitution

Answer 2

thats as far as I can do

Answer 3

1. from 2nd equation, 3(x-y)=12 --> (x-y)=4
from 1st equation:-x+y=-4--->(x-y)=4
so basically both the equations are same and there will be no solution.
no solution----> inconsistent system.
clear with 1st ??

Answer 4

Yes inconsistent for first

Answer 5

oh wait i am sorry,
there are infinitely many solutions for 1.
infinitely many--->dependent and consistent.

Answer 6

Ok cool, and whats the second one?

Answer 7

2. from 2nd eq:15y-6x=-24
so, 5y-2x=-8
so 2x-5y=8
which is same as 1st equation.
so this case is also same case as 1.
so infinitely many solutions.
so dependent and consistent .

Answer 8

So consistent and dependent? You positive?

Answer 9

yes,absolutely.
did u get why infinite solutions?

Answer 10

No, why?

Answer 11

lets take 1. as example.
both equations gave this :x-y=4
which means any values of x,y which satisfies x-y=4 are the solutions.
like (5,1)(6,2)(7,3).....and so on till infinity.
hence infinite solution,got it?