Question

(a;b)=18; 7a+3b=1512​

Answer 1

Explicație pas cu pas:

(a;b)=18 => a=18x si b=18y

7a+3b=1512 => 7*18*x+3*18*y=1512 => 18(7x+3y)=1512 =>

7x+3y=84

7x+3y=84 => 7x=84-3y => 7x=3(28-y) => 3|7x<=>3|x

Avem cazurile:

x=3 => 21+3y=84 => 3y=63 => y=21 => a=54 si b=5778 (fals)

x=6 => 42+3y=84 => 3y=42 => y=14 => a=108 si b=252 (solutie adevarata pentru ca verifica ecuatia)

x=9 => 63+3y=84 => 3y=21 => y=7 =>a=162 si b=126

(adevarat)

x=12 => 84+3y=84 => 3y=0 => y=0 (fals)

deci (a,b)€{(108,252),(162,126)}