Question 305382: Good Morning Algebra.com,
I have a question for you again and would appreciate your help
Post a fifty word response to the following
o How do you know when an equation has infinitely many solutions?
o How do you know when an equation has no solution?
Again Thank you for you help!
The needy one :)
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! If the number of variables is more than the number of equations, there are an infinite number of solutions.
x = 6 has one solution.
x+y = 6 has an infinite number of solutions.
------------------
You asked about "an equation", I think you meant a system of equations.
--------------
x + y = 2
x - 2y = 10 has one solution.
--------------
x + y = 2
2x + 2y = 4 has an infinite number, the 2nd eqn is 2x the 1st --> dependent.
-------------
x + y = 2
x + y = 3 has no solution --> inconsistent.
------------------
x + y + z = 3
x + y - z = 1 has an infinite number, only 2 eqns with 3 variables.
-------------
|
|
|
