SOLUTION: 7x + 10y = 1 -7x + -10y =-1 is this a no solution or infinitely many? I got infinitely many. Thank u

Algebra ->  Equations -> SOLUTION: 7x + 10y = 1 -7x + -10y =-1 is this a no solution or infinitely many? I got infinitely many. Thank u      Log On


   

Question 1162295: 7x + 10y = 1
-7x + -10y =-1
is this a no solution or infinitely many?
I got infinitely many.
Thank u
Found 3 solutions by Boreal, MathTherapy, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply the bottom by -1, and it becomes 7x+10y=1, which is the same as the top. Infinite solutions

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

7x + 10y = 1
-7x + -10y =-1
is this a no solution or infinitely many?
I got infinitely many.
Thank u
Add the 2 equations and you should get: 0 +- 0 = 0. 

This is a true statement, so YES, INFINITELY MANY solutions exist in this case.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

These two equations are  EQUIVALENT  to each other.

It means that you have,  actually,  one equation for two variables.

It has  INFINITELY  many solutions.

You can take any value for one variable and then adjust the second value to have true solution to one equation
(and hence for both equations).

Geometrically,  these two equations represent one line  (the same line)  in a coordinate plane;
all the points of this line represent infinitely many solutions.


That's all.