# Linear Diophantine equations of several variables

I know how to solve Diophantine equations of the form $ax+by=c$ but how can I solve linear Diophantine equations having more variables. Like what are the integer solutions of $43x+23y-435z+1324w=1$? I tried to substitute $t=43x+23y-435z$ and then solve first $t+1324w=1$ but then I found that as the result depends on another parameter, it won't help to solve the original equation.

• Are you trying to solve the equation without multiple parameters? – Ethan Hunt Apr 14 '16 at 16:33
• There can be multiple parameters. I just want to know all solutions and how to find them. – curious Apr 14 '16 at 16:48