1. $\left\{\begin{array}{l}2 x+y=-10 \\ x-3 y=2\end{array}\right.$

Step 1 ：Multiply the first equation by 3 and the second equation by 1 to make the coefficients of y equal: \(\begin{cases} 6x + 3y = -30 \\ x - 3y = 2 \end{cases}\)

Step 2 ：Add the two equations to eliminate y: \(7x = -28\)

Step 3 ：Divide by 7 to find x: \(x = -4\)

Step 4 ：Substitute x back into one of the original equations to find y: \( -4 - 3y = 2 \)

Step 5 ：Solve for y: \(y = -2\)

Step 6 ：\(\boxed{x = -4, y = -2}\)