The problem in the image consists of solving the following system of equations:

1. $x + y = 5$
2. $x - 2y = -4$

Step 1: Solve one equation for one variable

From the first equation, $x + y = 5$, solve for $x$: $x = 5 - y$

Step 2: Substitute into the second equation

Substitute $x = 5 - y$ into $x - 2y = -4$: $(5 - y) - 2y = -4$ Simplify: $5 - 3y = -4$

Step 3: Solve for $y$

$-3y = -4 - 5$ $-3y = -9$ $y = 3$

Step 4: Substitute $y = 3$ back into $x = 5 - y$

$x = 5 - 3$ $x = 2$

Final Solution:

The solution to the system of equations is: $x = 2, \; y = 3$

Let me know if you'd like me to verify this solution or explain further.

Here are 5 related questions to expand this concept:

1. How do we solve a system of equations graphically?
2. What are other methods to solve systems of equations, such as substitution and elimination?
3. Can systems of equations have no solutions or infinitely many solutions? How do we identify these cases?
4. How would you solve a system of equations with more than two variables?
5. What real-life problems can be modeled and solved using systems of equations?

Tip: Always double-check your substitutions to avoid errors when solving systems of equations!