Question

Determinati cifrele x si y stiind ca :
x, (y6)₊y, (6x)₊6,(xy)=x₊y₊7.

Answer 1

x,(y6)+y,(6x)+6,(xy)=x+y+7

x,(y6)=(xy6-x)/99=(100x+10y+6-y)/99=(99x+10y+6)/99=x+ (10y+6)/99

y,( 6x)=(y6x-y)/99=(100y+60+x-y)/99=(99y+60+x)/99=y+ (60+x)/99

6,(xy)= (6xy-6)/99=(600+10x+y-6)/99=(594+10x+y)/99=6+ (10x+y)/99

=> x,(y6)+y,(6x)+6,(xy)= x+ (10y+6)/99 + y+ (60+x)/99 +6+ (10x+y)/99

x+y+6+ (10y+6+60+x+10x+y)/99 =x+y+7

=> (11x+11y+66)/99=1

(x+y+6)/9=1

=> x+y+6=9; x+y=3

(x; y) ={(0; 3); (1; 2); (2; 1); (3; 0)}