Question

Aflati doua nr. x si y , stiind ca:
a. x-y=10 si x/y=5/3
b. 3x-y=12 si x/y=3/5

Answer 1

a. 3x=5y => x= 5y/3
x-y=10 => 5y/3 - y = 10 => 5y- 3y = 30 => 2y = 30 => y = 15; x= 25

b. 5x= 3y => x=3y/5
3x-y= 12 => 9y/5 - y = 12 => 9y-5y = 60 => 4y=60 => y= 15 ; x = 9

Answer 2

a. x=5y/3
⇒5y/3-y=10
⇒5y/3-3y/3=10
⇒2y/3=10
⇒2y=3·10⇒2y=30⇒y=30/2⇒y=15;
⇒x=5y/3
⇒x=5·15/3⇒x=5·5⇒x=25;
Verificare 25-15=10;
sau y=3x/5
⇒x-3x/5=10
⇒5x/5-3x/5=10
⇒2x/5=10⇒2x=5·10⇒2x=50⇒x=50/2⇒x=25;
⇒y=3x/5⇒y=3·25/5⇒y=3·5⇒y=10;
Verificare 25-15=10;
b. x=3y/5
⇒3·3y/5-y=12
⇒9y/5-y=12
⇒9y/5-5y/5=12
⇒4y/5=12⇒4y=5·12⇒4y=60⇒y=60/4⇒y=15;
⇒x=3y/5
⇒x=3·15/5⇒x=3·3⇒x=9;
Verificare 3·9-15=27-15=12;
sau y=5x/3
⇒3x-5x/3=12
⇒9x/3-5x/3=12
⇒4x/3=12⇒4x=12·3⇒4x=36⇒x=36/4⇒x=9;
⇒y=5x/3
⇒y=5·9/3
⇒y=5·3⇒y=15;
Verificare 3·9-15=27-15=12;