Questions on Algebra: Linear Algebra (NOT Linear Equations) answered by real tutors!

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Question 163534: this is a question on 3x3 systems
i need 3 seperate problems for this one question which is:
The sum of three numbers is 57. The second is 3 more than the first. The third is 6 more than the first. Find the numbers. I have no idea how to set this up. Please help. thank you.
: this is a question on 3x3 systems
i need 3 seperate problems for this one question which is:
The sum of three numbers is 57. The second is 3 more than the first. The third is 6 more than the first. Find the numbers. I have no idea how to set this up. Please help. thank you.

Answer by Fombitz(1799) About Me  (Show Source):
You can put this solution on YOUR website!
First, name your variables.
How about A, B, and C?
Then turn the words into mathematical equations.
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"The sum of three numbers is 57."
1.A+B+C=57
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"The second is 3 more than the first."
2.B=A+3
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"The third is 6 more than the first."
3.C=A+6
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Now substitute eq. 2 and eq. 3 into eq. 1 and solve for A.
1.A+B+C=57
A+(A+3)+(A+6)=57
3A+9=57
3A=48
highlight(A=16)
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Now that you have A you can find B and C using eq. 2 and eq. 3,
2.B=A+3
B=16+3
highlight(B=19)
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3.C=A+6
C=16+6
highlight(C=22)
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Check your answer.
A+B+C=57
16+19+22=57
57=57
True statement.
Good answers.