The system of linear equations provided is:

$2x + 5y = -10$ $2x - y = 8$

To solve this system, we can use the elimination or substitution method. I'll proceed with the elimination method by removing $x$.

Step 1: Eliminate $x$

Subtract the second equation from the first:

$(2x + 5y) - (2x - y) = -10 - 8$ $2x + 5y - 2x + y = -18$ $6y = -18$

Step 2: Solve for $y$

$y = \frac{-18}{6} = -3$

Step 3: Substitute $y = -3$ into one of the original equations to solve for $x$

Using the second equation:

$2x - (-3) = 8$ $2x + 3 = 8$ $2x = 5$ $x = \frac{5}{2} = 2.5$

Solution

The solution to the system is: $x = 2.5, \quad y = -3$

Would you like more details on any specific step, or do you have any further questions?

Here are five related questions to consider:

1. How would the solution change if we used the substitution method instead?
2. What is the graphical interpretation of this solution?
3. Can this system of equations be represented in matrix form?
4. How can we verify the solution by substituting back into both equations?
5. What happens to the solution if one of the equations changes?

Tip: Always verify your solutions by substituting them back into the original equations to ensure accuracy.