Question

Rezolvati prin metoda substitutiei urmatoarele sisteme de ecuatii:​

Answer 1

Răspuns:

Explicație pas cu pas:

Rezolvati prin metoda substitutiei urmatoarele sisteme de ecuatii:​

6(x-y)+3y+5=2x    ⇔6x-6y+3y-2x=-5   ⇔4x-3y=-5  ⇔4x=3y-5  ⇒x=(3y-5)/4

8(x-2y)+4=3x-10y  ⇔8x-16y-3x+10y=-4  ⇔5x-6y=-4 ⇒

x=(3y-5)/4

5·(3y-5)/4-6y=-4  ⇔15y-25-24y=-16  ⇔-9y=25-16  ⇔-9y=9  ⇔y=-1

x=(3y-5)/4=(-3-5)/4=-8/4=-2     x=-2

Answer 2

$\it 6(x-y)+3y+5=2x \Rightarrow 6x-6y+3y+5-2x=0 \Rightarrow 4x-3y=-5\ \ \ \ \ (1)\\ \\ 8(x-2y)+4=3x-10y \Rightarrow 8x-16y+4-3x+10y=0 \Rightarrow 5x-6y=-4\ \ \ (2)\\ \\ Adun\breve am\ ecua\c{\it t}iile\ (1)\ \d si\ (2)\ \d si\ vom\ avea:\\ \\ 9x-9y=-9\bigg|_{:9} \Rightarrow x-y=-1 \Rightarrow x=y-1\ \ \ \ (3)\ \ (rela\c{\it t}ia\ de\ substitu\c{\it t}ie)$

$\it (1),\ (3) \Rightarrow 4(y-1)-3y=-5 \Rightarrow 4y-4-3y=-5 \Rightarrow y=-1\ \ \ \ \ (4)\\ \\ (3),\ (4) \Rightarrow x=-1-1 \Rightarrow x=-2\\ \\ S=\{(-2,\ -1)\}$