Question

Without graphing is the system independent, dependent, or inconsistent?
-2x-y=9
3x-4y=-8
Could someone please explain

Answer 1

is equation 2 multiple of equation 1 ?

Answer 2

Not sure what you mean by a multiple

Answer 3

Inconsistent equations are those which have no common solution: parallel lines.
Dependent equations are 2 different ways of expressing the same line: infinite # of solutions. Independent equations have one ordered pair solution: they cross at one point.

Answer 4

equation 1 -2x-y=9
equation 2 \( a \times (-2x-y)= a \times 9 \)
if you have such type of system, then it is dependent.

Answer 5

So, try to solve for y in terms of x in the first equation and substitute into the next equation and see where this takes you.

Answer 6

I dont understand how to work the problems out to figure the answer, these are new to me

Answer 7

if you don't have above type of systems then it is independent system.

Answer 8

equation 1: \( −2x−y=9 \)
equation 2: \( a×(−2x−y)=c\) where \( c≠a×9 \)
if you have such type of system, then it is inconsistent..

Answer 9

if i did it right i got y=-2x-9 and y=3x/4+2

Answer 10

Good. Now, set both equation = to each other and solve for x.

Answer 11

i ended up with x=-4 and y=-1

Answer 12

Very good. You have a unique, one-point solution, so you have independent equations. And you're done!

Answer 13

Picturing the system of the 2 equations in your mind's eye, since you're told not to graph, you can picture two lines that intersect at one point.

Answer 14

if you have a problem that says no solution would that be considered inconsistent

Answer 15

yes

Answer 16

okay, thank you for helping me really appreciate it

Answer 17

And if the system is of two variables, they are parallel lines on a flat plane in the Euclidean model, the one we think of automatically. The "real-world" model.

Answer 18

You're quite welcome and thx for the medal recognition.

Answer 19

your welcome