Question 81155: Solve the following system 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)   (Show Source):
You can put this solution on YOUR website! Solve the following system by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.
:
2x + 3y = 1
5x + 3y = 16
:
Multiply the 1st equation by -1 and add the two equations:
-2x - 3y = -1
5x + 3y = 16
------------- adding, eliminates y
+3x + 0y = +15
:
x = 15/3
x = +5
:
Find y by substituting 5 for x in the 1st equation:
2x + 3y = 1
2(5) + 3y = 1
10 + 3y = 1
3y = 1 - 10; subtracted 10 from both sides
3y = -9
y = -9/3
y = -3
:
:
Check solutions in the 2nd equation by substituting both solutions:
5x + 3y = 16
5(5) + 3(-3) =
25 - 9 = +16
:
It's unique solution is: x=5, y=-3
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