{6x+2y=12 și {x-4y=-11

[tex]\left\{\begin{matrix}
6x + 2y = 12 \: | \div 2 \\

x - 4y = - 11\end{matrix}\right.[/tex]

[tex]\left\{\begin{matrix}
3x + y = 6 \: | \times 4 \\

x - 4y = - 11\end{matrix}\right.[/tex]

[tex]\left\{\begin{matrix}
12x + 4y = 24\\

x - 4y = - 11\end{matrix}\right.[/tex]

[tex]12x + x + 4y - 4y = 24 - 11[/tex]

[tex]13x = 13 \: | \div 13[/tex]

[tex]x = 1[/tex]

[tex]3x + y = 6[/tex]

[tex]3 \times 1 + y = 6[/tex]

[tex]3 + y = 6[/tex]

[tex]y = 6 - 3[/tex]

[tex]y = 3[/tex]

[tex] \left \{ {{6x+2y=12 |\cdot 2} \atop {x-4y=-11}} \right. [/tex]

[tex] \left \{ {{12x+4y=24} \atop {x-4y=-11}} \right. [/tex]

[tex](12x+4y)+(x-4y)=24+(-11)[/tex]

[tex]12x+4y+x-4y=24-11[/tex]

[tex]13x=13 \Rightarrow x=1[/tex]

[tex]2y=12-6x;~ 2y=12-6\cdot 1;~ 2y=6;~ y=6:2;~ \Rightarrow y=3[/tex]