The given system of equations is:

1. $x + y = 25$
2. $x - y = 5$

To solve for $x$ and $y$, we can use the method of elimination or substitution. Here is the step-by-step solution:

Step 1: Add the two equations

$(x + y) + (x - y) = 25 + 5$ $2x = 30$ $x = 15$

Step 2: Substitute $x = 15$ into one of the original equations

Substitute into $x + y = 25$: $15 + y = 25$ $y = 10$

Final Answer:

$x = 15, \, y = 10$

Would you like me to explain further or explore related concepts? Here are some related questions:

1. What happens if we use substitution instead of elimination to solve the system?
2. Can you solve a similar system with negative coefficients?
3. What is the graphical interpretation of this solution?
4. How would this method change if fractions were involved?
5. Can you verify the solution using a matrix method?

Tip: Always check your solutions by substituting them back into the original equations to ensure they satisfy