Question

Dacă 9x - 4y supra 2x + 3y = 2 atunci x supra y este ​

Answer 1

Răspuns:

Explicație pas cu pas:

(9x - 4y) / (2x + 3y) = 2

9x - 4y = 2(2x + 3y)

9x - 4y = 4x + 6y

9x - 4x = 6y + 4y

5x = 10y

x/y = 10/5 = 2

Answer 2

 

$\displaystyle\bf\\\frac{9x-4y}{2x+3y} =2\\\\Fractia~o~simplificam~fortat~cu~y.\\\\\frac{\dfrac{9x-4y}{y}}{ \dfrac{2x+3y}{y}} =2\\\\\\\frac{\dfrac{9x}{y}-\dfrac{4y}{y}}{\dfrac{2x}{y}+\dfrac{3y}{y}} =2\\\\\\\frac{9\cdot\dfrac{x}{y}-4\cdot\dfrac{y}{y}}{2\cdot\dfrac{x}{y}+3\cdot\dfrac{y}{y}} =2\\\\\\Substitutie:\\\\\boxed{\bf\frac{x}{y}=a}\\\\\\\frac{9a-4}{2a+3}=2\\\\\\9a-4=2(2a+3)\\\\9a-4=4a+6\\\\9a-4a=6+4\\\\5a=10\\\\a=\frac{10}{5}\\\\ a=2\\\\\frac{x}{y}=a=2\\\\\boxed{\bf\frac{x}{y} =2}$