Question

{6x+2y=12 și {x-4y=-11

Answer 1

$\left\{\begin{matrix} 6x + 2y = 12 \: | \div 2 \\ x - 4y = - 11\end{matrix}\right.$

$\left\{\begin{matrix} 3x + y = 6 \: | \times 4 \\ x - 4y = - 11\end{matrix}\right.$

$\left\{\begin{matrix} 12x + 4y = 24\\ x - 4y = - 11\end{matrix}\right.$

$12x + x + 4y - 4y = 24 - 11$

$13x = 13 \: | \div 13$

$x = 1$

$3x + y = 6$

$3 \times 1 + y = 6$

$3 + y = 6$

$y = 6 - 3$

$y = 3$

Answer 2

$\left \{ {{6x+2y=12 |\cdot 2} \atop {x-4y=-11}} \right.$

$\left \{ {{12x+4y=24} \atop {x-4y=-11}} \right.$

$(12x+4y)+(x-4y)=24+(-11)$

$12x+4y+x-4y=24-11$

$13x=13 \Rightarrow x=1$

$2y=12-6x;~ 2y=12-6\cdot 1;~ 2y=6;~ y=6:2;~ \Rightarrow y=3$