Question

stiind ca x-3ysupra x+2y=1supra4 determinati 2x-ysupra x+2y​

Answer 1

 

$\displaystyle\\ \frac{x-3y}{x+2y}=\frac{1}{4}\\\\\\\frac{2x-y}{x+2y}=?\\\\\text{Rezolvam sistemul:}\\\\x-3y=1~~~\Big|~\cdot(-1)\\x+2y=4\\........\\-x+3y=-1\\x+2y=4\\..................\text{Adunam ecuatiile:}\\/~~5y=3\\\\y=\boxed{\frac{3}{5}}\\\\x+2y=4\\x+2\cdot\frac{3}{5}=4\\\\x+\frac{6}{5}=4\\x=4-\frac{6}{5}=\frac{20-6}{5}=\boxed{\frac{14}{5}}$

$\displaystyle\\ \text{inlocuim in fractia:}~~\frac{2x-y}{x+2y}=?\\\\\\\frac{2x-y}{x+2y}=\frac{2\cdot\dfrac{14}{5}-\dfrac{3}{5}}{\dfrac{14}{5}+2\cdot\dfrac{3}{5}}=\frac{\dfrac{28}{5}-\dfrac{3}{5}}{\dfrac{14}{5}+\dfrac{6}{5}} =\frac{~~\dfrac{28-3}{5}}{\dfrac{14+6}{5}~~}=\frac{~~\dfrac{25}{5}~~}{~~\dfrac{20}{5}~~}=\frac{25}{20}=\boxed{\boxed{\bf\frac{5}{4}}}$

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