Question 513406: Solve for (a,b,c,d)
a+b+c=0
b+c+d=1
a+c+d=2
a+b+d=3
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Solve for (a,b,c,d)
a + b + c = 0
b + c + d = 1
a + c + d = 2
a + b + d = 3
:
Subtract the 2nd equation from the 1st equation
0 + b + c + d = 1
a + b + c + 0 = 0
------------------- subtraction eliminates b and c
-a + d = 1
d = (a + 1)
:
Subtract the 2nd equation from the 3rd equation
a + b + 0 + d = 3
0 + b + c + d = 1
--------------------subtraction eliminates b and d
a - c = 2
-c = -a + 2
c = (a - 2)
:
Use the 3rd equation
a + c + d = 2
replace c and d, find a
a + (a-2) + (a+1) = 2
3a = -1 = 2
3a = 2 + 1
3a = 3
a = 1
then
c = a-2
c = 1 - 2
c = -1
and
d = a + 1
d = 1 + 1
d = 2
:
Find b using the 1st equation
a + b + c = 0
1 + b -1 = 0
b = 0
:
:
Summarize a=1, b=0, c=-1, d=2
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