Question

Is this system consistent or inconsistent?
2x + y = 5
-4x + 6y = 12

Answer 1

Have you attempted to find solutions? It almost always helps to simplify where possible. That second equation can be prettied up a bit.

2x + y = 5
-2x + 3y = 6

Now, you can just add the two equations and see what gives.

Answer 2

wait did you divide the second equation by two?

Answer 3

Each term had a factor of 2. It seemed a good idea if my goal was to simplify my life.

Answer 4

okay let me solve

Answer 5

I still don't get it my 2x cancelled but I don't think im suppose to get a remainder

Answer 6

fractions are fine

Answer 7

okay good! so once I get my fraction then what do I do?

Answer 8

you have found y?,

well then, sub it into one of those equations at the top and find x

Answer 9

y is 2 3/4. so how do I know if is consistent or dependent?

Answer 10

yes that is y , what is x?


if there is at least one solution (x,y) then the system consistent

if there are no possible solutions the system is inconsistent

Answer 11

x is 1.125 or 1.12 1/2

Answer 12

right?

Answer 13

so these answers would be a solution?

Answer 14

Consistent: ANY solution.
Inconsistent: NO Solution.

Answer 15

yes x is 1.125

Answer 16

so its consistent because I found an answer?

Answer 17

that's it

Answer 18

okay thank you :)

Answer 19

if you had a system like

x + y = 1
x + y = 0

taking the difference

0 = 1 ???

this system is inconsistent because no matter what values x and y are ,
both equations cannot be satisfied simultaneously

Answer 20

I understand it now thank you! how do find out if a system is dependent or not?
like 2x + y = 4 and -6x - 3y = -12

Answer 21

try to find a solution like last time, what happens

Answer 22

both the variable cancel ou

Answer 23

out

Answer 24

and we are

Answer 25

eft

Answer 26

left

Answer 27

left with 0 = 0

Answer 28

Yes, that is right

Answer 29

both equations are the equation to the same straight line

Answer 30

so there are infinitely many solutions so its dependent

Answer 31

can you do one more?

Answer 32

-x + 4y = 24 -2x + 8y = 8

Answer 33

-x + 4y = 24
-2x + 8y = 8

Answer 34

you might start by doubling the first equation

Answer 35

okay ill get right on that

Answer 36

answer is 0 = 56 not dependent

Answer 37

0 = 56 inconsistent

Answer 38

confused

Answer 39

it doesn't make sense to say wether a system is dependent or not if is isn't even consistent

Answer 40

I think we should back to the last one (the dependent system), because you got the right answer but i think the reasoning was incorrect

Answer 41

2x + y = 4
-6x - 3y = -12

this system reduced to

y = -2x+4
0 = 0

yes there are infinite solutions , (but some systems with infinite solutions are dependent)

the system is dependant because

y is a function of x y(x)=-2x+4
___



if we had a system

x=x
y=0

this system also has infinite solutions, but this is an independent system

this system is independent because y is not a function of x

Answer 42

oh okay thank you I get it