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
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2) 4r -6s +6t = 1
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3) r +s +t = 1
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multiply equation 3 by 6 and add to equation 2 to eliminate variable s
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4) 10r +12t = 7
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multiply equation 1 by 2 and add to equation 2 to sliminate variable s
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5) 8r +30t = 9
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solve equations 4 and 5 for r and t
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solve equation 5 for r and substitute in equation 4
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r = (9 -30t)/8
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10(9 -30t)/8 +12t = 7
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90 -300t +96t = 56
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-204t = -34
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t = 34/204 = 17/102
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r = (9 -30(17/102))/8 = 1/2
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use equation 3 to solve for s
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1/2 +s +17/102 = 1
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s = 34/102 = 1/3
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r = 1/2, s = 1/3, t = 17/102
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check the answers
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equation 1
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2(1/2) +3(1/3) +12(17/102) = 4
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1 +1 +2 = 4
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4 = 4
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equation 2
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4(1/2) -6(1/3) +6(17/102) = 1
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2 -2 +1 = 1
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1 = 1
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equation 3
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1/2 +1/3 +17/102 = 1
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51/102 + 34/102 +17/102 = 1
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102/102 = 1
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1 = 1
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answers check
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