diophantine linear equation with condition on the sum of coefficients [closed]

I am trying to solve the following diophantine equation

x*a + y*b == c

where a,b,c are integers and the absolute value of their sums is, for instance, 4. Then I like to plot the results in the x,y plane.

Is it possible with FindInstance or Reduce ? Thanks.

closed as off-topic by MarcoB, m_goldberg, user9660, Öskå, JensJul 1 '16 at 4:14

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• Reduce[{x*a + y*b == c, Abs[a + b + c] == 4}, {x, y}, Integers] returns a result, albeit somewhat complex. Perhaps you could start from there. – MarcoB May 29 '16 at 3:40
• What do you mean by "plot the results in the x,y plane"? What kind of plot do you envision? What will be the independent and dependent variable? What parameters? – m_goldberg Jun 30 '16 at 0:34