What are all tuples off postive integers w,x,y,z that fullfill following system of equations: x+10z^2=2014, 2y+z=54, (y+2x+7/2w)z=1211

Marley Meyers

Marley Meyers

Answered question

2022-10-26

What are all tuples off postive integers w , x , y , z that fullfill following system of equations:
x + 10 z 2 = 2014
2 y + z = 54
( y + 2 x + 7 2 w ) z = 1211

Answer & Explanation

Gael Irwin

Gael Irwin

Beginner2022-10-27Added 13 answers

One approach is to use basic detective work. From the second equation, z is even. Now look at the first equation x + 10 z 2 = 2014. Since z is even and positive, there are not many possibilities for z. For already at z = 20 we have 10 z 2 is quite a bit bigger than 2014.
So there are not many cases to check. A bit grungy, but you will soon arrive at the solution.
By the way, 1211 = ( 7 ) ( 173 ). If you think about this, you will arrive at the answer in one step.

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