We are given the system of two linear equations:

$\text{1) } 2x + y = 7$ $\text{2) } x - 2y = 6$

To solve this system, we can use either substitution or elimination. Here, I'll use substitution.

Step 1: Solve one equation for one variable

From equation (2), solve for $x$:

$x = 6 + 2y$

Step 2: Substitute this expression for $x$ into equation (1)

Substitute $x = 6 + 2y$ into the first equation $2x + y = 7$:

$2(6 + 2y) + y = 7$

Simplify:

$12 + 4y + y = 7$

$12 + 5y = 7$

Step 3: Solve for $y$

Subtract 12 from both sides:

$5y = 7 - 12$

$5y = -5$

Divide by 5:

$y = -1$

Step 4: Substitute $y = -1$ back into the expression for $x$

Substitute $y = -1$ into $x = 6 + 2y$:

$x = 6 + 2(-1) = 6 - 2 = 4$

Step 5: Final solution

The solution to the system is:

$x = 4, \, y = -1$

So, the solution is $(x, y) = (4, -1)$.

Would you like any further explanation or clarification?

Here are 5 related questions to explore:

1. How would the solution change if the system of equations had no solution?
2. Can you solve the same system using the elimination method?
3. What is the geometric interpretation of the solution to this system of equations?
4. How would you solve the system if both equations were nonlinear?
5. How can you check if the solution to the system is correct?

Tip: Always substitute your solution back into the original equations to verify if it satisfies both equations!