Question

Rezolvati sistemul prin metoda reducerii sau a substitutiei :
2x-3y-4=0
-3x+10y+6=0

Answer 1

Răspuns:

2x-3y-4 = 0 =>2x-3y =4

-3x+10y+6=0 => -3x+10y= -6

{2x-3y=4  | * (-10)

{ -3x+10y =-6 | * |+3)

..................................

-20x +30y= -40

- 9x + 30y = -18

...................................... ( - )

-11x= -22 => x=2

2x-3y=4 => 2*2-3y=4 => 4-3y=4

3y=0 => y=0

{x=2

{y=0

Answer 2

Metoda I:

$\left \{ {{2x-3y-4=0} \atop {-3x+10y+6=0}} \right. \\\left \{ {{2x-3y=4 /*3} \atop {-3x+10y=-6/*2}} \right.\\\\\left \{ {{6x-9y=12} \atop {-6x+20y=-12}} \right. \\--------\\0+11y=0\\=>y=0\\6x-9y=12\\6x-9*0=12\\6x=12\\x=2$

Metoda II

$\left \{ {{2x-3y-4=0} \atop {-3x+10y+6=0} \right. \\\left \{ {{2x-3y=4} => 2x=4+3y=>x=\frac{4+3y}{2} \\\atop \\{-3x+10y=-6}} \right.\\-3*\frac{4+3y}{2} +10y=-6\\\frac{-12-9y}{2}+10y=-6\\-12-9y+20y=-12\\11y=0\\y=0\\x=(4+3y):2\\x=4:2\\x=2$