Question

Several systems of equations are given below.

Answer 1

@iGreen. @Directrix

Answer 2

@DanJS

Answer 3

Here is a quick reference page on the meaning of each of those types of systems.
http://www.algebra.com/algebra/homework/coordinate/Types-of-systems-inconsistent-dependent-independent.lesson

Answer 4

Ya but idk how to graph inequalities

Answer 5

These are equalities, system of two lines. You have to be able to tell if each one is either,
-parallel lines
-the same line in two forms
-intersecting lines

Answer 6

1. parellel 2. intersecting 3. the same line in two forms :P

Answer 7

That is what those fancy words pretty much mean...

a) Consistent and Independent = Has 1 unique solution (x,y), and Not the same line, cross at one point.

b) Consistent and Dependent = Infinitely many solutions, the same line overlapped, if you solve, you will get something like 10 = 10, True Statement.

c) Inconsistent = parallel lines, no solutions, if you solve you will get a false statement like 13=5, false.

Answer 8

ok so maybe system 2 is consistent independent

Answer 9

System 1:

y = 6x - 1.5
y = -6x + 1.5

Answer 10

ohhh so its the first :P

Answer 11

If you tried to solve System 1, you can set y = y to get,

6x - 1.5 = -6x + 1.5
12x = 3
x = 1/4 = 0.25

Has a unique single solution, it is Consistent, and Independent.

Answer 12

ohhh that actually makes some sense

Answer 13

Soooo B?

Answer 14

System 2 is

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

Answer 15

To see this by looking at the equations. You can put them both in y = mx+b form,

They will both have the same slope m.
They will have different intercepts b.

Answer 16

ahhh ok :D so its what in slope intercept and can we do c? @DanJS

Answer 17

or you can leave them as is, and you can see that the coefficients on X and Y are a multiple of one another.

Multiply the first equation by 2, and you get the same left side as the second.

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

Same Left side = Parallel lines

Answer 18

so it has no solutions correct

Answer 19

System 3 is similar to system 2, but when you multiply the first equation by a constant, you get BOTH left and right sides the same... like this

2x - y = 5 (multiply eq1 by 3)
6x - 3y = 15
---------------

6x - 3y = 15
6x - 3y = 15

same line, infinitely many solutions,
Dependent

Answer 20

To recap..

System 1 = Single Solution, Consistent - Independent

System 2 = No Solution, Inconsistent - Independent

System 3 = Infinite Solutions, Consistent - Dependent

Answer 21

System 1 - Crossing Lines

System 2 - Parallel Lines

System 3 - Same Single Line

Answer 22

i just wrote this -

3.

System 1 is Consistent independent and has 1 solution. This is because
6x-1.5=-6x+1.5
12x=3
x=1/4= 0.25
x=0.25
y=0
This has a single solution, and it is consistent- independent.
The single point of intersection is- (0.25,0)

b.
System 2-
x+3y=-6
2x+6y=-3

System 2 has Parallel lines, and No Solutions/ intersections.
Therefore, It is Inconsistent- No solutions/ parallel
Independent- Not the Same line.

The coefficients on x and y are multiples of each other. So All I have to do is multiply the first equation by two. and you get the same exact left side as the second.
2x+6y=-12
2x+6y=-3
Same left Side= Parallel Lines

c.

System 3 is almost like system 2 but when I multiply the first equation by a constant, I get BOTH left and ride sides the exact same.

2x-y=5
6x-3y=15
_________
6x-3y=15
6x-3y=15
same line, infinitely many solutions
dependents.

Answer 23

Good?

Answer 24

Looks good to me. Just study this page , all the stuff is on there http://www.algebra.com/algebra/homework/coordinate/Types-of-systems-inconsistent-dependent-independent.lesson

Answer 25

:D kk i will can we do another New ? so i can give u new medal

Answer 26

Sure i can do one more... link me to it