solve the linear system

x+2y=6

-7x+3y=-8

$\begin{array}{rcll} (1) & x+2y &=& 6 \qquad & | \qquad \cdot 7 \\ (1) & 7x+14y &=& 42 \\ (2) & -7x+3y &=& -8 \\ \\ \hline \\ (1) +(2) & 7x - 7x + 14 y + 3 y &=& 42 - 8 \\ & 14 y + 3 y &=& 42 - 8 \\ & 14 y + 3 y &=& 34 \\ & 17 y &=& 34 \qquad & | \qquad : 17 \\ & y &=& \frac{ 34 }{17} \\ & \mathbf{y} & \mathbf{=} & \mathbf{2} \\ \\ \hline \\ (1) & x+2y &=& 6 \qquad & y = 2 \\ & x+2\cdot 2 &=& 6 \\ & x+4 &=& 6 \\ & x+4 &=& 6 \qquad & | \qquad -4 \\ & x &=& 6 -4 \\ & \mathbf{x} & \mathbf{=} & \mathbf{2} \\ \end{array}$