Question

Ajutatima varog multt mult ? urgent .

Answer 1

1) fie x=1
rezulta y=3
deci o solutie este (1;3)


2) adunam membru cu membru
 3x=-3
x=-1
y=-4-x= -4+1=-3
 deci (x;y) =(-1;-3)
restul in atasament

Answer 2

[tex]1.2x+y=5\\ Deoarece\ 2x\ este\ par\ si\ 5\ este\ impar,inseamna\ ca\ y\ este\ impar.\\ Pentru\ y=3\Rightarrow x=1\\ (x,y)=(1,3)\\ \\ 2. \left \{ {{2x-y=1} \atop {x+y=-4}} \right.\Leftrightarrow \left \{ {{2x-y=1} \atop {2x+2y=-8}} \right.\\ Prin\ scadere\ obtinem: /-3y=9\Rightarrow y=-3\\ 2x+3=1\\ 2x=-2\Rightarrow x=-1\\ S:(x,y)=(-1,-3)\\ \\ 3. \left \{ {{3x-2\ \textless \ 7} \atop {4-2x\leq 3x+14}} \right. \\ Rezolvam\ fiecare\ inecuatie\ separat:\\ 3x-2\ \textless \ 7\Rightarrow x\ \textless \ 3\Rightarrow S_1=(-\infty,3)\\ [/tex]
[tex]4-2x\leq 3x+14\\ -5x \leq 10\Rightarrow x\geq -2\Rightarrow S_2=[-2,\infty)\\ S=S_1\cup S_2=[-2,3)\\ Asadar:x\in \{-2,-1,0,1,2\}\\ \\ 4.a)6x^2+0,5x=0\\ x(6x+0,5)=0\\ \Rightarrow x_1=0\\ \Rightarrow 6x+0,5=0\\ 6x=-\frac{1}{2}\\ x_2=-\frac{1}{12}\\ S:x\in \{0,-\frac{1}{12}\}\\ b)3x^2+13x-10=0\\ \Delta=169+120=289\Rightarrow \sqrt{\Delta}=17\\ x_1=\frac{-13+17}{6}=\frac{2}{3}\\ x_2=\frac{-13-17}{6}=-5\\ S:x\in \{\frac{2}{3},-5\}\\ c)5x(5x+2)+3=2\\ 25x^2+10x+1=0\\ (5x+1)^2=0\Rightarrow S:x=-\frac{1}{5}\\ [/tex]

[tex]5.Aplicam\ relatii\ lui\ Viet\acute{e}:\\ S=x_1+x_2=6\\ P=x_1\cdot x_2=(3-\sqrt2)(3+\sqrt2)=3-2=1\\ \boxed{x^2-Sx+P=0}\\ x^2-6x+1=0\\ \\ 6.Not\breve{a}m: x=num\breve{a}rul\ b\hat{a}rnelor\ de\ stejar\\ ~~~~~~~~~~~~~~~y=num\breve{a}rul\ b\hat{a}rnelor\ de\ brad\\ \left \{ {{x+y=300} \atop {46x=28y-1000}} \right. \Leftrightarrow \left \{ {{x+y=300} \atop {46x-28y=-1000}} \right. \Leftrightarrow \left \{ {{46x+46y=13800} \atop {46x-28y=-1000}} \right. \\ [/tex]
[tex]Dac\breve{a}\ sc\breve{a}dem\ relatiile\ obtinem:/74y=14800\Rightarrow y=200\\ x+200=300\Rightarrow x=100\\ R:100\ b\hat{a}rne\ de\ stejar\ si\ 200\ b\hat{a}rne\ de\ brad[/tex]