The problem involves solving the system of equations:

1. $y = x + 5$
2. $x + y = 3$

Solution:

Step 1: Substitute $y = x + 5$ into $x + y = 3$. $x + (x + 5) = 3$

Step 2: Simplify the equation. $2x + 5 = 3$

Step 3: Solve for $x$. $2x = 3 - 5$ $2x = -2$ $x = -1$

Step 4: Use $x = -1$ to find $y$ using $y = x + 5$. $y = -1 + 5$ $y = 4$

Final Answer:

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

Would you like me to explain any step further?

Here are 5 related questions to expand your understanding:

1. How do you graphically solve systems of linear equations like this one?
2. What are the properties of a consistent and independent system of equations?
3. How can you solve a system of equations using matrix methods (e.g., substitution vs. elimination)?
4. What happens if the two equations describe parallel lines?
5. How do systems of equations apply to real-world scenarios, like budgeting or physics?

Tip: Always check your solution by substituting both values back into the original equations.