SOLUTION: Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent. 2x+3y=1 5x+3y=16 and x+5y=10 -2

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent. 2x+3y=1 5x+3y=16 and x+5y=10 -2      Log On


   

Question 59064: Solve each of the following systems by addition. If a unique solution does not exist, state
whether the system is inconsistent or dependent.
2x+3y=1
5x+3y=16
and
x+5y=10
-2x-10y= -20
thank you
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Solve each of the following systems by addition. If a unique solution does not exist, state
whether the system is inconsistent or dependent.
L1) 2x+3y=1
L2) 5x+3y=16
Multiply either L1 or L2 by -1 and add it to L1 and the y's will be eliminated and you can solve for x. I'm going with L2:
L2) -1(5x+3y)=-1(16) ---->> -5x-3y=-16
:
2x+3y=1
-5x-3y=-16
__________
-3x=-15
-3x/-3=-15/-3
x=5
Substitute that into either L1 or L2 and solve for y. I'm going with L1:
2(5)+3y=1
10+3y=1
-10+10+3y=-10+1
3y=-9
3y/3=-9/3
y=-3
The unique solution is: (5,-3)
:::::::::::::::::::::::::::::::::
and
L1)x+5y=10
L2)-2x-10y= -20
Multiply L1 by 2 and add to L2 in an attempt to eliminate the x's.
L1) 2(x+5y)=2(10)---->> 2x+10y=20
2x+10y=20
-2x-10y=-20
___________
0+0=0
0=0
There is no unique solution for this one. because 0 does = 0 this one is dependent. It has an infinite number of solutions because graphically they are the same line and have all points in common.
Happy Calculating!!!