Question

Rezolvat prin metoda substitutiei :
$\left \{ {{X+Y=10} \atop {2X-Y=8}} \right.$

Answer 1

x+y=10 => x=10-y

2x-y=8 <=> 2(10-y)-y=8 <=> 20-2y-y=8 <=> 20-3y=8 => -3y=-12 => y=4.

x=10-y=10-4=6.

Solutie: (x,y)=(6,4).

Answer 2

[tex] \left \{ {{x+y=10} \atop {2x-y=8}} \right. [/tex] ⇔$\left \{ {{x=10-y} \atop {2(10-y)-y=8}} \right.$ ⇔$\left \{ {x=10-y} \atop {20-2y-y=8}} \right.$ ⇔ $\left \{ {{x=10-y} \atop {20-y=8}} \right.$ ⇔$\left \{ {{x=10-y} \atop {y=20-8}} \right.$ ⇔$\left \{ {{x=10-y} \atop {y=12}} \right.$ ⇔ $\left \{ {{x=10-12} \atop {y=12}} \right.$ ⇔$\left \{ {{x= -2} \atop {y=12}} \right.$