Diofant equation

In the set of integers (Z) solve the equation:

$212x+316y=0$

Write result with integer parameter

$t\in Z$

(parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)

Correct answer:

x =  -79 t
y =  53 t

Step-by-step explanation:

$$\begin{gathered} GCD(212,316)=4 \\ {\displaystyle \frac{x}{y}}=-{\displaystyle \frac{316}{212}}=-{\displaystyle \frac{79}{53}}=-{\displaystyle \frac{79t}{53t}} \\ x=-79t \\ y=53t \\ t\in Z \end{gathered}$$

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