To solve this system of linear equations:

$2x + y = 7$ $3x - 2y = -11$

we can use either the substitution or elimination method. I'll proceed with the elimination method here.

Step 1: Eliminate $y$

1. Multiply the first equation by 2 to make the coefficients of $y$ opposites:

   $2 \times (2x + y) = 2 \times 7$ $4x + 2y = 14$

2. Rewrite the equations:

   $4x + 2y = 14$ $3x - 2y = -11$

3. Add these equations together to eliminate $y$:

   $(4x + 2y) + (3x - 2y) = 14 + (-11)$ $7x = 3$

4. Solve for $x$:

   $x = \frac{3}{7}$

Step 2: Substitute $x = \frac{3}{7}$ into the first equation to solve for $y$

1. Substitute $x = \frac{3}{7}$ into the first equation:

   $2\left(\frac{3}{7}\right) + y = 7$

2. Simplify:

   $\frac{6}{7} + y = 7$

3. Subtract $\frac{6}{7}$ from both sides:

   $y = 7 - \frac{6}{7} = \frac{49 - 6}{7} = \frac{43}{7}$

Solution

The solution to the system is: $x = \frac{3}{7}, \quad y = \frac{43}{7}$

Would you like more details or have any questions?

Here are 5 additional questions related to this topic:

1. How do we verify the solution for a system of linear equations?
2. Can we solve this system using the substitution method instead?
3. How would we express this system in matrix form?
4. How can graphing help in visualizing the solution to a linear system?
5. How do we apply the elimination method to systems with more than two variables?

Tip: To avoid calculation errors, double-check each step, especially when dealing with fractions.