You poured some $10 \%$ alcohol solution and some $8 \%$ alcohol solution into a mixing container. Now you have 500 grams of $8.56 \%$ alcohol solution. Write and solve a system of equations to find how many grams of $10 \%$ solution and how many grams of $8 \%$ solution you poured into the mixing container.
You mixed $\square$ grams of $10 \%$ solution with $\square$ grams of $8 \%$ solution.

Step 1 ：Let's denote the amount of $10 \%$ solution as x and the amount of $8 \%$ solution as y.

Step 2 ：We can set up two equations to represent the total weight and the total alcohol content.

Step 3 ：The total weight equation would be \(x + y = 500\).

Step 4 ：The total alcohol content equation would be \(0.10x + 0.08y = 0.0856 \times 500\).

Step 5 ：Solving this system of equations gives us the values of x and y.

Step 6 ：The solution to the system of equations is \(x = 140\) and \(y = 360\).

Step 7 ：This means that 140 grams of $10 \%$ solution and 360 grams of $8 \%$ solution were mixed to get 500 grams of $8.56 \%$ solution.

Step 8 ：Final Answer: You mixed \(\boxed{140}\) grams of $10 \%$ solution with \(\boxed{360}\) grams of $8 \%$ solution.