Question

You graph a system of equations and the two lines overlap, or lie right on top of one another. Explain what this tells you about the:

solution to the system
the two equations
the result if the system was solved algebraically

Answer 1

Please @wolf1728 help me with this last one!

Answer 2

Thanks wolf you came at the right time my mom is on my butt man i need to finish this last question quick

Answer 3

If the two lines lie one atop the other, the equations are said to be equivalent. (One equation can easily be transformed to the other by algebraic manipulation).
Example of equivalent equations:
x + y = 9
3x + 3y = 27

If two lines are parallel to each other, the equations are said to be inconsistent.
Example
2x + 2y = 6
2x + 2y = 8

If the equations are equivalent or inconsistent, they cannot be solved.
If equations are inconsistent, when solved algebraically they produce mathematical impossibilities.
For example, solving the above 2 equations produces the result that 6 = 8.

Solving equivalent equations:
A) x + y = 9
B) 3x + 3y = 27
We'll multiply equation A by -3
A) -3x -3y = -27 and add that to B
B) 3x + 3y = 27
which results in nothing.

Answer 4

Gee, I got a little carried away on that answer.
:-)

Answer 5

Lmao you did i'm not sure which part i should take for my answer

Answer 6

If the graph of both lines lie one atop the other, there will be no solution.
The equations are said to be equivalent.
If solved algebraically, the result is nothing. (Not too sure about that last sentence)

Answer 7

From above:

Solving equivalent equations:
A) x + y = 9
B) 3x + 3y = 27
We'll multiply equation A by -3
A) -3x -3y = -27 and add that to B
B) 3x + 3y = 27
which results in nothing.

Answer 8

Take that too?

Answer 9

That is a summary of the longer paragraph I typed. Yes, include the equivalent equation part.

Answer 10

Okay so for this question I put If the graph of both lines lie one on top of the other, there will be no solution.The equations are said to be equivalent.
If solved algebraically the result will be nothing.

Solving equivalent equations:
A) x + y = 9
B) 3x + 3y = 27
We'll multiply equation A by -3
A) -3x -3y = -27 and add that to B
B) 3x + 3y = 27
which results in nothing.

Answer 11

I guess that is a good summary. I just don't like that expression of "this results in nothing". (Doesn't sound very mathematical).

Answer 12

Loll any other way of putting it?

Answer 13

I suppose not.

Answer 14

How about it sums up to nothing or zero?

Answer 15

Well I guess you could say that

Answer 16

So you think this is all I need to as the answer?

Answer 17

Well looking at the question at the top:
*** solution to the system
It has no solution

***the two equations
they are equivalent

***the result if the system was solved algebraically
It adds to nothing - there is no algebraic solution.

Answer 18

So should I write this instead and take out the other ones?

Answer 19

I'll leave that up to you - it's your class, your grade, etc

Answer 20

Well you kind of already answered it for me I'm just saying should i add the examples you were giving me

Answer 21

At least the equivalent equation example. The inconsistent example is really not covered in that question.

Answer 22

Thats cool. this is what i put now f the graph of both lines lie one on top of the other, there will be no solution.The equations are going to be equivalent.
If solved algebraically the result will be nothing.
when solving equivalent equations:
A) x + y = 9
B) 3x + 3y = 27
We'll multiply equation A by -3
A) -3x -3y = -27 and add that to B
B) 3x + 3y = 27
which sums up to nothing.

Answer 23

No the equations ARE equivalent not they are going to be ...

Change "when solving equivalent equations" to
"Example of trying to solve equivalent equations"

Answer 24

oh ok

Answer 25

all set then?

Answer 26

Yeah man Thanks big time

Answer 27

I can always count on you

Answer 28

that's okay
:-)

Answer 29

:) Goodnight

Answer 30

good night