Question

Given the equation 4x + 2y = 9, which equation below would cause an inconsistent-independent system?

6x + 12y = 13

2x + y = -6

x - 2y = 7

8x - 4y = -5

Answer 1

inconsistent means there's no shared point on the lines
aka the lines are parallel

Answer 2

You mean there isn't going to be any solution?

Answer 3

the lines in an inconsistent system will not get any solution
we pick the line that has no solution with line in problem statement

Answer 4

I don't know which one that is.

Answer 5

8x - 4y = -5 <- this one isn't it, the slope is different

2x + y = -6 (*2)
4x + 2y = -12
^
this one looks exactly the same like the one in the problem statement
it has a different solution even though it has the same amounts of y, x
that means there's a contradiction and the system is inconsistent

Answer 6

Where did you get 4x + 2y = -12 from?

Answer 7

Is it an example?

Answer 8

from 2x + y = -6
I multiplied it by 2

Answer 9

LHS and RHS - every term x2

Answer 10

Ohhh

Answer 11

:)

Answer 12

So that's the answer?

Answer 13

yes

Answer 14

Thanks.

Answer 15

no problem.

Answer 16

whats the answer

Answer 17

@realmadridCR7 inconsistent means that there is never a shared point.
the x-y pair the one needs doesn't work in the other. there is not a single x-y pair that both equations will satisfy.
so the system of equations can never be satisfied, the system is inconsistent.

Answer 18

dependent means ,that the second equation is just a "derived form" of the first, so that second equation "depends" on the first one, example:

y= 2x + 3 #first equation
2y = 4x + 6 #second equation

The second line is the first line multiplied by two. It is not a new arrangement - it is just multiplied by 2, and it is the first one multiplied by two, so it DEPENDS on the first one.

Answer 19

you have to compare this equation 4x + 2y = 9 with all the other equations, and determine if there is one that will be parallel; and if it is parallel, then the second requirement is that it's not a multiple of 4x + 2y = 9.