Răspuns:
[tex]a) {\bf S=\{(2,9)\}}, \ b){\bf S=\{(1,3)\}}[/tex]
[tex]c)\bf S=\{(2,7)\}, \ d)\bf S=\{(5,2)\}[/tex]
Explicație pas cu pas:
[tex]a)\begin{cases} 4x-y=-1\\2x+y=13\end{cases}[/tex]
[tex]4x+2x = -1+13 \Rightarrow 6x=12 \Rightarrow x = 2[/tex]
[tex]8-y=-1 \Rightarrow y=8+1 \Rightarrow y=9[/tex]
[tex]\Rightarrow \bf S=\{(2,9)\}[/tex]
[tex]b)\begin{cases}x+y=4 \ \big|\cdot(-1)\\3x+y=6 \end{cases} \Rightarrow \begin{cases}-x-y=-4\\3x+y=6 \end{cases}[/tex]
[tex]-x+3x=-4+6 \Rightarrow 2x=2 \Rightarrow x=1[/tex]
[tex]1+y=4 \Rightarrow y=4-1 \Rightarrow y = 3[/tex]
[tex]\Rightarrow \bf S=\{(1,3)\}[/tex]
[tex]c)\begin{cases}x-y=-5\\-x+3y=19 \end{cases}[/tex]
[tex]-y+3y=-5+19 \Rightarrow 2y=14 \Rightarrow y = 7[/tex]
[tex]x-7=-5 \Rightarrow x = -5+7 \Rightarrow x = 2[/tex]
[tex]\Rightarrow \bf S=\{(2,7)\}[/tex]
[tex]d)\begin{cases}3x+2y=19\\x+5y=15\ \big|\cdot(-3) \end{cases} \Rightarrow \begin{cases}3x+2y=19\\-3x-15y=-45 \end{cases}[/tex]
[tex]2y-15y=19-45 \Rightarrow -13y = -26 \Rightarrow y = 2[/tex]
[tex]x+10=15 \Rightarrow x=15-10 \Rightarrow x = 5[/tex]
[tex]\Rightarrow \bf S=\{(5,2)\}[/tex]
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