Question

$Daca \frac{3x+4y}{2x+y} = \frac{7}{3} , atunci \frac{x}{y} = ?$

$Daca \frac{6x+4y}{5x+2y} = \frac{3}{2} , atunci \frac{x}{y} = ?$

$Daca \frac{5x-4y}{2x-y} = \frac{7}{3} , atunci \frac{x}{y} = ?$

Answer 1

1. $\frac{3x+4y}{2x+y} = \frac{7}{3}$
Inmultim pe diagonala si se obtine : 7(2x+y)=3(3x+4y)⇒ 14x+7y=9x+12y⇒14x-9x=12y-7y⇒5x=5y. Impartim toata ecuatia la 5⇒ x=y ⇒ $\frac{x}{y}$=1

2. $\frac{6x+4y}{5x+2y}= \frac{3}{2}$
Procedam ca la primul si inmultim pe diagonala :
3(5x+2y)=2(6x+4y) ⇒ 15x+6y=12x+8y ⇒ 15x-12x=8y-6y⇒3x=2y⇒ $\frac{x}{y} = \frac{2}{3}$

3. $\frac{5x-4y}{2x-y}= \frac{7}{3}$
Inmultim pe diagonala : 
3(5x-4y)=7(2x-y) ⇒ 15x-12y=14x-7y⇒15x-14x= -7y+12y⇒ x= 5y ⇒ $\frac{x}{y}$=5