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How many solutions are there for this equation: $$x_1 + x_2 + x_3 = 17$$ when they are all non negative integers and $x_1 > 6$.

I was thinking to solve the original equation then subtracting $x_1 + x_2 + x_3 = 11$ from it. Would this be the appropriate path?

R.W
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jillon
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1 Answers1

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Almost. Since $x2$ and $x3$ are allowed to be zero, you should subtract $7$ from $x1$ and solve $x1+x2+x3=10$ in the nonnegative integers. That way all the variables are treated the same.

Ross Millikan
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  • I don't really get why it's 7. If x1 was instead x1 >= 6 would we then use 6? – jillon Apr 03 '17 at 02:45
  • Because the minimum allowable value for $x1$ is $7$ and the other variables are allowed to be $0$. We want to allow the new $x1$ (I would have given it a different name) to be $0$ as well. Yes, if you had said $x1 \ge 6$ I would have subtracted $6$. In addition, if you had said $x2$ and $x3$ had to be positive instead of nonnegative I would have subtracted $6$. – Ross Millikan Apr 03 '17 at 02:50