MAML, Matrices, Determinants and Systems of Equations: Sums of Variables
1This is a MAML (Maine Association of Math Leagues) problem from October 2010 (Meet 1 of 2012-13), Round 3, Problem 2: http://maml.net/problems.htm
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Condensed Writing Solution:
We need to solve for x+y+z using the following equations: 3x+y=17, 5y+z=14, 3x+5z=41
Thus, first, we will add all of the equations together to get 6x+6y+6z=72:
3x+1y+0z=17
+0x+5y+1z=14
+3x+0y+5z=41
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6x+6y+6z=72
Now, just factor out the 6 and divide by 6 to get our answer
6(x+y+z)=72
x+y+z=12 ANSWER