Question

a)Cho 8x+3y chia hết 11 
Chứng minh x-y chia hết cho 11
b) Cho 4x+3y chia hết cho 13
Chứng minh 7x+2y chia hết cho 13

Answer 1

a) \(8x+3y⋮11\Leftrightarrow7\left(8x+3y\right)⋮11\)(vì \(\left(7,11\right)=1\))

\(\Leftrightarrow\left[\left(56x-5.11x\right)+\left(21y-2.11y\right)\right]⋮11\)

\(\Leftrightarrow\left(x-y\right)⋮11\).

b) \(\left(4x+3y\right)⋮13\Leftrightarrow5\left(4x+3y\right)⋮13\)(vì \(\left(5,13\right)=1\))

\(\Leftrightarrow\left[\left(20x-13x\right)+\left(15y-13y\right)\right]⋮13\)

\(\Leftrightarrow\left(7x+2y\right)⋮13\).