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

Algebra ->  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      Log On


   

Question 103425: 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
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
2x + 3y = 1
5x + 3y = 16
:
Multiply the 1st equation by -1 and add
-2x - 3y = -1
5x + 3y = 16
-----------------add
3x + 0y = 15
3x = 15
x = 15/3
x = 5
:
Find y using the 1st equation:
2x + 3y = 1
2(5) + 3y = 1
10 + 3y = 1
3y = 1 - 10
3y = -9
y = -9/3
y = -3
:
Check solutions using the 2nd equation
5x + 3y = 16
5(5) + 3(-3) = 16
25 - 9 = 16; confirms our solutions