SOLUTION: Solve the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent. x + 5y = 10 -2x - 10y = -20

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent. x + 5y = 10 -2x - 10y = -20       Log On


   

Question 63064This question is from textbook
: Solve the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.
x + 5y = 10
-2x - 10y = -20
 This question is from textbook

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.
E1: x + 5y = 10
E2: -2x - 10y = -20
Multiply E1 by 2 and add it to E2.
E1: 2(x+5y)=2(10) --> 2x+10y=20
:
2x+10y=20
-2x-10y=-20
____________
0+0=0
0=0
When all your variables are eliminated, you have one of two cases, 0=0 means that the system is dependent. The lines are lying right on top of each other and there are infinitely many solutions because they have all points in common.
:
:
If both your variables are eliminated and your left with 0=(something other than 0). Then you would have had an inconsitent system. The lines would be parallel and never intersect, thus giving no solution.
:
Happy Calculating!!!