SOLUTION: My book says this is for systems of equations in three variables, the elimination method. Question: How do I solve 2r+3s+12t=4,4r-6s+6t=1,r+s+t=1? I have tried to combine the firs

Question 1142658: My book says this is for systems of equations in three variables, the elimination method. Question: How do I solve 2r+3s+12t=4,4r-6s+6t=1,r+s+t=1? I have tried to combine the first 2 formulas, eliminating opposites and collecting like terms and then using that answer to add to the third formula(r,s,t=1) but there are no opposites. I'm stumped. Please and thank you!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
1) 2r +3s +12t = 4
:
2) 4r -6s +6t = 1
:
3) r +s +t = 1
:
multiply equation 3 by 6 and add to equation 2 to eliminate variable s
:
4) 10r +12t = 7
:
multiply equation 1 by 2 and add to equation 2 to sliminate variable s
:
5) 8r +30t = 9
:
solve equations 4 and 5 for r and t
:
solve equation 5 for r and substitute in equation 4
:
r = (9 -30t)/8
:
10(9 -30t)/8 +12t = 7
:
90 -300t +96t = 56
:
-204t = -34
:
t = 34/204 = 17/102
:
r = (9 -30(17/102))/8 = 1/2
:
use equation 3 to solve for s
:
1/2 +s +17/102 = 1
:
s = 34/102 = 1/3
:
********************************
r = 1/2, s = 1/3, t = 17/102
:
check the answers
:
equation 1
:
2(1/2) +3(1/3) +12(17/102) = 4
:
1 +1 +2 = 4
:
4 = 4
:
equation 2
:
4(1/2) -6(1/3) +6(17/102) = 1
:
2 -2 +1 = 1
:
1 = 1
:
equation 3
:
1/2 +1/3 +17/102 = 1
:
51/102 + 34/102 +17/102 = 1
:
102/102 = 1
:
1 = 1
:
answers check
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