Question

Rezolvați prin metoda substitutiei:
2x-y=1
x+3y=4

Answer 1

Răspuns:

x=1

y=1

Explicație pas cu pas:

2x-y=1

x+3y=4  (inmultim cu 2)

2x-y=1

2x+6y=8

(scadem ecuatiile)

/-7y=-7

y=1

2x-y=1 (inmultim cu 3)

x+3y=4

6x-3y=3

x+3y=4

(adunam ecuatiile)

7x=7

x=1

Answer 2

$\it \begin{cases}\it 2x-y=1 \Rightarrow 2x-1=y \Rightarrow y=2x-1\ \ \ \ (*) \\ \\ \it x+3y=4 \stackrel{(*)}{\Longrightarrow}\ x+3(2x-1)=4 \Rightarrow x+6x-3=4 \Rightarrow 7x=7 \Rightarrow x=1\end{cases}\\ \\ \\ x=1\stackrel{(*)}{\Longrightarrow}\ y=2-1=1\\ \\ \\ S=\{(1,\ \ 1)\}$