SOLUTION: Have I correctly stated the 3 graph equations correctly? 1. Two equations whose graphs are identical lines are called DEPENDENT equations. 2. Two or more equations that hav

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Question 1170593: Have I correctly stated the 3 graph equations correctly?
1. Two equations whose graphs are identical lines are called DEPENDENT equations.
2. Two or more equations that have one common solution are called SIMULTANEOUS equations.
3. Two equations whose graphs are parallel lines are called INCONSISTENT equations.
I think I have these equations listed correct above - just want to make sure I have identified these 3 equations correctly.
Thank you
Found 3 solutions by Theo, ikleyn, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
number 1 is correct.

number 2 is not.

two or more equations that have one common solution are called independent equations.

number 3 is correct.

i got this from the following reference.

https://courses.lumenlearning.com/boundless-algebra/chapter/systems-of-equations-in-two-variables/

the above applies to straight line equations.

those are equations where the highest exponent of the independent variable is 1.

such an equations will have the standard form of ax + by = c
a is the coefficient of the x term.
b is the coefficient of the y term.
c is the constant term.

if the value of x is 0, then this becomes by = c
if the value of y is 0, then this becomes ax = c

if the exponent of x is 0, then this becomes a + by = c
if the exponent of y is 0, then this becomes ax + b = c

the value of both x and y can't be equal to 0 because then you have 0 = c which is not a line.

the exponent of both x and y can't be equal to 0 because then you have a + b = c which is not a line.
Answer by ikleyn(52847)   (Show Source): You can put this solution on YOUR website!
.

(1)  The answer is  DEPENDENT.     Your answer is correct.



(2)  The answer is CONSISTENT.     This term is applied if there is a unique solution OR more than one solution 
                                   (including infinitely many solutions).
                                   In other words, this term is used, when there is AT LEAST one solution.


     The other term which is applied/applicable for linear equations, too, is  INDEPENDENT.   
                                    This term is used, when the system of linear equations has ONLY ONE solution.


     Your answer is incorrect.



(3)  The answer is INCONSISTENT.   Your answer is correct.


Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

Have I correctly stated the 3 graph equations correctly?
1. Two equations whose graphs are identical lines are called DEPENDENT equations.
2. Two or more equations that have one common solution are called SIMULTANEOUS equations.
3. Two equations whose graphs are parallel lines are called INCONSISTENT equations.
I think I have these equations listed correct above - just want to make sure I have identified these 3 equations correctly.
Thank you
2. A consistent system or consistent equations since they have at least one solution, and

   an independent system or independent equations because they have EXACTLY ONE solution.

   Therefore, you can choose one, the other, or both!! 

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