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Question

Solve in positive integers:
12x11y+4z=22
4x+5y+z=17.

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Solution

12x11y+4z=221
4x+5y+z=172
multiplying by 3 in equation 2 and adding equation 1

12x11y+4z=22
12x+15y+3z=51
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯4y+7z=73

737z4

Now, putting this value in equation 1
12x11(737z4)+4z=22
48a+803+77z+16z=88
48x+93z=891

x=89193z48

So, the general solutions are
{(89193z48),(737z4),z} Now, putting z=7,
x=5,y=6,z=7

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