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Old 08-06-2007   #2
Alex Cabo
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Ok, let us start with the problem.18x+23y+52z+69w=530x+y+z+w=20but now we have too many variables, so we eliminate one, the 'y' has a prime coefficient so that one should go first. We set the second equation equal to 'y'y=20-x-z-wand substitute in the first.18x+23(20-x-z-w)+52z+69w=53018x+460-23x-23z-23w+52z+69w=530(18x-23x)+(52z-23z)+(69w-23w)=530-460-5x+29z+46y=70 We still have too many variables but there is nothing we can do about it so we have to think. . . (the answer is obvious, but the reasoning goes like this) 29+46=75...-5 =70! so x=1,z=1,w=1 and we can now substitute in the original equationx+y+z+w=201+y+1+1=20y+3=20y=20-3y=17and we corroborate our result:18(1)+23(17)+52(1)+69(1)=53018+391+52+69=53 0409+121=530530=530Q.E.D.