To solve this system of equations:

$3x - 2y = 1$ $x + 2y = 11$

we can use the method of elimination or substitution. Here’s how to proceed with elimination:

1. Add both equations together to eliminate $y$:

   $(3x - 2y) + (x + 2y) = 1 + 11$ $4x = 12$

2. Divide by 4 to solve for $x$:

   $x = 3$

3. Substitute $x = 3$ back into the second equation to find $y$:

   $3 + 2y = 11$ $2y = 8$ $y = 4$

Solution

The solution to the system is: $x = 3, \quad y = 4$

Would you like more details on any step?

Here are five related questions to expand your understanding:

1. What if the equations had different coefficients for $y$? How would that affect the elimination method?
2. How would substitution work in solving this system?
3. Can you verify the solution by substituting $x = 3$ and $y = 4$ back into the original equations?
4. What are some situations where graphing the equations might be useful?
5. How would you solve this system if it were in three dimensions with an additional equation?

Tip: Always double-check by substituting your values into both original equations to ensure they satisfy each equation.