Round #1005

Solve the system: 2x + 3y = 12 and x - y = 1.

```csharp using System; class Program { static void Main() { // Given equations // 2x + 3y = 12 // x - y = 1 // Solve the second equation for x // x = y + 1 // Substitute x into the first equation // 2(y + 1) + 3y = 12 // Expand and simplify // 2y + 2 + 3y = 12 // 5y + 2 = 12 // Subtract 2 from both sides // 5y = 10 // Divide by 5 // y = 2 // Now that we have y, substitute it back into the equation x = y + 1 // x = 2 + 1 // x = 3 Console.WriteLine("x = 3, y = 2"); } } ```

To solve the system, we can use substitution or elimination. Let's use substitution. Rearrange the second equation to isolate x: x = 1 + y. Substitute this expression for x into the first equation: 2(1 + y) + 3y = 12. Expand and simplify: 2 + 2y + 3y = 12, which becomes 5y = 10. Solve for y: y = 2. Now substitute y back into the equation x = 1 + y: x = 1 + 2, so x = 3. Therefore, the solution to the system is x = 3 and y = 2.