Solve the system by any method. (If there is no solution, enter NO sOLUTION. If there are an infinite number of solutions, enter the general solution in terms of $x$, where $x$ is any real number.) \[ \begin{array}{r} 0.1 x+0.2 y=4 \\ 0.35 x-0.3 y=0 \end{array} \]

Step 1 ：Given the system of equations: \[\begin{array}{r} 0.1 x+0.2 y=4 \\ 0.35 x-0.3 y=0 \end{array}\]

Step 2 ：First, multiply the first equation by 0.35 and the second equation by 0.1 to make the coefficients of x in both equations the same: \[\begin{array}{r} 0.035 x+0.07 y=1.4 \\ 0.035 x-0.03 y=0 \end{array}\]

Step 3 ：Subtract the second equation from the first to eliminate x: \[0.1 y = 1.4\]

Step 4 ：Solve for y: \[y = 14\]

Step 5 ：Substitute y = 14 into one of the original equations to find x: \[0.1 x + 0.2(14) = 4\]

Step 6 ：Solve for x: \[x = 12\]

Step 7 ：The solution to the system of equations is \(x = 12\) and \(y = 14\)

Step 8 ：Final Answer: \[\boxed{x = 12, y = 14}\]