Question

Consistent or Inconsistent ?

Answer 1

8x +Y+4 = 0
y=8x - 4

Answer 2

@madrockz are you available to help?

Answer 3

I think its Consistent

Answer 4

solve them maybe.

if u have 1 or more solutions, it is consistent.
if u have NO solutions, it is incosistent.

Answer 5

@ganeshie8 both are the problem :/

Answer 6

tbh, i wont solve it.
i see that both have different slopes. So they WILL intersect at some point. that guarantees a solution.

Answer 7

having a solution => system is consistent.

Answer 8

@ganeshie8 I'm not a asking you to solve it, how do you setup the equation

Answer 9

im saying, u dont have to solve it.
just by interpreting slopes, we can conclude here :)

Answer 10

i mean, u dont have to solve the equations all the way.
just interpret the slopes and conclude

Answer 11

Ok thanks can you help with 2 more problems I will tell you what I think and you can point me in a direction @ganeshie8

Answer 12

shoot

Answer 13

Lol ?? @ganeshie8

Answer 14

i mean shoot the question lol

Answer 15

*Ask the question

Answer 16

7x + 6 = -2y
-14x -4y + 2 = 0

I think if inconsistent @ganeshie8

Answer 17

is sorry

Answer 18

change equations to slope intercept form :-

7x + 6 = -2y => y = -7/2x - 3
-14x -4y + 2 = 0 => y = -7/2x + 1/2

they have same slopes, but diff intercepts.
so they never meet.

Answer 19

so it is inconsistent ?

Answer 20

https://www.youtube.com/watch?v=Ix8Nne-a-KQ

Answer 21

Consistent and Inconsistent Systems of Equations
All the systems of equations that we have seen in this section so far have had unique solutions. These are referred to as Consistent Systems of Equations, meaning that for a given system, there exists one solution set for the different variables in the system or infinitely many sets of solution. In other words, as long as we can find a solution for the system of equations, we refer to that system as being consistent

For a two variable system of equations to be consistent the lines formed by the equations have to meet at some point or they have to be parallel.

For a three variable system of equations to be consistent, the equations formed by the equations must meet two conditions:

All three planes have to parallel
Any two of the planes have to be parallel and the third must meet one of the planes at some point and the other at another point.
Given that such systems exist, it is safe to conclude that Inconsistent systems should exist as well, and they do. Inconsistent Systems of Equations are referred to as such because for a given set of variables, there in no set of solutions for the system of equations.

Inconsistent systems arise when the lines or planes formed from the systems of equations don't meet at any point and are not parallel (all of them or only two and the third meets one of the planes at some point.)

Two variable system of equations with Infinitely many solutions
The equations in a two variable system of equations are linear and hence can be thought of as equations of two lines. When these two lines are parallel, then the system has infinitely many solutions.

When two lines are parallel, their equations can usually be expressed as multiples of each other and that's usually a quick way to spot systems with infinitely many solutions.

For example, let's try to solve the system of equations below:



Using substitution method, we can solve for the variables as follows:

From equation (1)



substituting the above into equation(2)







In the above equation, we can see that we've lost all the variables from the equation. This means that we can pick any value of x or y then substitute it into any one of the two equations and then solve for the other variable.

For example if we pick x = 0, then if we substitute this into equation (1) we would get y = 1. Any value we pick for x would give a different value for y and thus there are infinitely many solutions for the system of equations.

Two variable systems of equations with NO SOLUTION
There also exist two variable system of equations with no solution at all. This happens when as we attempt to solve the system we end up an equation that makes no sense mathematically.

For example, solve the system of equations below:



Using matrix method we can solve the above as follows:



Reducing the above to Row Echelon form can be done as follows:



Adding row 2 to row 1:



The equation formed from the second row of the matrix is given as



which means that:



But we know that the above is mathematically impossible. When we come across the above, we say that the system of equations has NO SOLUTION. Thus we refer to such systems as being inconsistent because they don't make any mathematical sense.

Three variable systems of equations with Infinite Solutions
When discussing the different methods of solving systems of equations, we only looked at examples of systems with one unique solution set. These are known as Consistent systems of equations but they are not the only ones. Three variable systems of equations with infinitely many solution sets are also called consistent.

Since the equations in a three variable system of equations are linear, they can also be thought of as equations of planes. The way these planes interact with each other defines what kind of solution set they have and whether or not they have a solution set. When these planes are parallel to each other, then the system of equations that they form has infinitely many solutions.

Just as with two variable systems, three variable sytems have an infinte set of solutions if when you solving for the variables you end up with an equation where all the variables disappear.

For example; solve the system of equations below:



Solution:

Using matrix method:









In the last row of the above augmented matrix, we have ended up with all zeros on both sides of the equations. This means that two of the planes formed by the equations in the system of equations are parallel, and thus the system of equations is said to have an infinite set of solutions. We solve for any of the set by assigning one variable in the remaining two equations and then solving for the other two.

For example, if we take y =3

Then:







Then using the first row equation, we solve for x





Three variable systems with NO SOLUTION
Three variable systems of equations with no solution arise when the planed formed by the equations in the system neither meet at point nor are they parallel. As a result, when solving these systems, we end up with equations that make no mathematical sense.

For example; solve the system of equations below



Solution:

Using Matrix method:







In the last row, we ended up with the equation 0 = 6 which we know can't be true and so we conclude that the system of equations has no solution.

Answer 22

@ganeshie8 Thanks one more an I will try the rest

Answer 23

-2x - 2y = 6
10x + 10y = -30 Consistent ??

Answer 24

np :) shoot it

Answer 25

inc

Answer 26

iconsistent

Answer 27

-2x - 2y = 6 => x+y = -3
10x + 10y = -30 => x+y = -3

Both are same equation. they're overlapping. that meand INFINITE solutions. so... ?

Answer 28

consistent lol

Answer 29

sorry for typoes lol hope u got wat i mean

Answer 30

yup !

Answer 31

Do you mine helping me with two more ? @ganeshie8 I got 20 Of this and getting the hang of it

Answer 32

good :) shoot

Answer 33

2y = x - 7
-2x - 6y = -14 consistent not sure

Answer 34

@ganeshie8

Answer 35

change both equations to y = mx + b form

Answer 36

consistent

Answer 37

clearly they have diff slopes.
that means they will intersect at some point --- a solution exists !

you're right

Answer 38

y = 2x + 5
-2x + y = -2 inconsistent for the last one

Answer 39

if u cud also tell me , why u think they're consistent, that helps me convince myself that you understood the thing :)

Answer 40

yes they're inconsistent. good job !

Answer 41

Thanks @ganeshie8 I hope ketch you on more often I really appreciate your help

Answer 42

catch

Answer 43

np :) you're wlcme :))

Answer 44

I let you know what I got on this assignment tomorrow @ganeshie8

Answer 45

hope u wil score 100% my best wishes to you :D