Question

ma puteti ajuta si pe mine sa rezolv sistemul asta? {x+2y=5 si 2x-5y=-4

Answer 1

$\displaystyle \left \{ {{x+2y=5| \cdot (-2)} \atop {2x-5y=-4}} \right. \Rightarrow \left \{ {{-2x-4y=-10} \atop {2x-5y=-4}} \right. \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-------- \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~/~~-9y=-14 \Rightarrow y= \frac{14}{9} \\ x+2 \cdot \frac{14}{9} =5 \Rightarrow x+ \frac{28}{9} =5 \Rightarrow 9x+28=5 \cdot 9 \Rightarrow \\ \\\Rightarrow9x+28=45 \Rightarrow 9x=45-28 \Rightarrow 9x=17 \Rightarrow x= \frac{17}{9}$