1,\(4x+5y=10\)
\(\Rightarrow x=\frac{10-5y}{4}\)
\(\Rightarrow x=\frac{8+2-4y-y}{4}\)
\(\Rightarrow x=2-y+\frac{2-y}{4}\)
Để x nguyên => 2-y=4k(k thuộc N*)
=> y = 2-4k
=> x = 2-2+4k+4k : 4
=> x = 4k+k
Vậy \(\left(x;y\right)\in\left(4k+k;2-4k\right).Với\forall k\inℕ^∗\)