Question

Rezolvati prin metoda reducerii si substitutiei sistemul de ecuatii: Dau Coroana si multe puncte Va rog frumos
2x+5y+6=0
4x+3y-9=0

Answer 1

2x+5y+6=0       se inmulteste cu (-2)  -4x-10y-12=0
4x+3y-9=0⇒                                         4x+3y-9=0⇒-7y-21=0⇒-7y=21⇒y=21/-7⇒y=-3
-4x-3-9=0⇒-4x=12⇒x=12/-4=x=3

Answer 2

$\left \{ {{2x=-6-5y} \atop {4x+3y-9=0}} \right. -\ \textgreater \ \left \{ {{2x=-6-5y} \atop {-12-10y+3y-9=0}} \right. -\ \textgreater \ \left \{ {{2x=-6-5y} \atop {-7y-21= 0 }} \right.$$\left \{ {{2x+5y+6=0} \atop {4x+3y-9=0}} \right.$   prima ecuatie din sistem se inmulteste cu (-2).  -> $\left \{ {{-4x-10y-12=0} \atop {4x+3y-9=0}} \right.$  4x si cu -4x se reduc -> adunam termenii care au ramas -> -10y+3y-9-12=0 ->  -7y -21=0 -> -7y =21 | impartim la -7. ->  y = -3.   Acum luam prima ecuatie din sistem si inlocuim y-ul cu -3.  -> 2x+5y+6 =0 -> 2x+5y = -6 -> 2x -15 = -6  -> 2x = -6 +15 -> 2x = 9 | impartim la 2 -> x = $\frac{9}{2}$   .. Testam si in  a doua ecuatie din sistem -> 4x+3y -9 = 0 -> 4x +3y=9    -> 4x -9 = 9  -> 4x = 18 | impartim la 4 -> x = $\frac{18}{4}$ -> simplificam cu 2  si rezulta x = $\frac{9}{2}$ asta e moteda reducerii... acm urmeaza metoda substitutiei.  ->$\left \{ {{2x=-6-5y} \atop {4x+3y-9=0}} \right. -\ \textgreater \ \left \{ {{2x=-6-5y} \atop {-12-10y+3y-9=0}} \right. -\ \textgreater \ \left \{ {{2x=-6-5y} \atop {-7y-21=0}} \right.$  -> -7y-21=0 -> -7y=21 ,impartim la -7 -> y=-3. si acum avem in sistem o varianta de a afla x-ul -> 2x=-5y-6 -> 2x = 15-6 -> 2x = 9  | impartim la 2 -> x = $\frac{9}{2}$