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rezolvati in multimea numerelor reale sistemul de ecuatii {2x-y=1x×2y=8​

Răspuns :

Andyilye

Răspuns:

x = 2, y = 3

Explicație pas cu pas:

[tex]\left \{ {{2x - y = 1} \atop {x + 2y = 8}} \right. \Big|^{(\cdot 2)}\iff \left \{ {{4x - 2y = 2} \atop {x + 2y = 8}} \right. \\ [/tex]

[tex]4x + x = 2 + 8[/tex]

[tex]5x = 10 \implies \bf x = 2[/tex]

[tex]2 + 2y = 8 \iff 2y = 8 - 2 \\ 2y = 6 \implies \it \bf y = 3[/tex]

Targoviste44

[tex]\it \begin{cases} \it 2x-y=1\\ \\ \it x+2y=8\end{cases}\\ \\ \\ x+2y=8 \Rightarrow 2y=8-x\ \ \ \ \ (1)\\ \\ 2x-y=1 \Rightarrow 2x-1=y \Rightarrow y=2x-1|_{\cdot2} \Rightarrow 2y=4x-2\ \ \ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow 4x-2=8-x \Rightarrow 4x+x=8+2 \Rightarrow 5x=10\Big|_{:5} \Rightarrow x=2\ \ \ \ \ (3)\\ \\ (1),\ (3) \Rightarrow 2y=8-2 \Rightarrow 2y=6\Big|_{:2} \Rightarrow y=3\\ \\ \\ S=\{(2,\ \ 3)\}[/tex]