Question

5x - 6y = -8 2x-9y= 10

Answer 1

Răspuns:

-4 si -2

Explicație pas cu pas:

5x - 6y = -8 I x2

2x-9y= 10 I x(-5) si le adunam(metoda reducerii):

10x - 12y - 10x + 45y = -16 - 50

33y = -66

y = -2

si inlocuim in cea de-a 2-a relatie pe y pt a-l afla pe x:

x = 10+9y  /  2 = 10-18  /  2 = -8/2 = -4

x = -4.

Verificare:

5x(-4) + 12 = -20 + 12 = -8, corect.

Answer 2

$\it 5x-6y=-8\ \ \ \ \ \ (1) \\ \\ 2x-9y=10\ \ \ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow 5x-2x-6x+9x=-8-10 \Rightarrow 3x+3y=-18|_{:3} \Rightarrow \\ \\ \Rightarrow x+y=-6 \Rightarrow x=-6-y\ \ \ \ \ \ \ (3)$

$\it (2),\ (3) \Rightarrow 2(-6-y)-9y=10 \Rightarrow \\ \\ \Rightarrow -12-2y-9y=10|_{+12} \Rightarrow -11y=22|_{:(-11)} \Rightarrow y=-2$

$\it y=-2\ \stackrel{(3)}{\Longrightarrow}\ x=-6+2=-4\\ \\ S=\{(-4,\ -2)\}$