Question 1123743: Solve the system by the addition method. Identify dependent systems.
2x + 3y = 5
3y = 5 - 2x Found 2 solutions by solver91311, Edwin McCravy:Answer by solver91311(24713) (Show Source):
If you put all of the terms of both equations on the same side of the equals sign, then you have two instances of the exact same equation. How would you expect the two solution sets to compare?
John
My calculator said it, I believe it, that settles it
2x + 3y = 5
3y = 5 - 2x
Add +2x to both sides of the second equation:
3y = 5 - 2x
+2x +2x
------------
3y+2x = 5
Swap the terms on the left side:
2x+3y = 5
So the system of equations is:
2x + 3y = 5
2x + 3y = 5
Multiply the second equation through by -1
and add the two equations vertically
term by term:
2x + 3y = 5
-2x - 3y = -5
-------------
0 - 0 = 0
0 = 0
When attempting to solve a system of equations,
if all the variable terms cancel, leaving only
purely numeric terms, then if the purely
numeric equation is true, the system of
equations is dependent, and if the purely
numeric equation is false, the system of
equations is inconsistent.
Since the purely numeric equation 0 = 0 is
true, the system is dependent.
Edwin
