The problem involves solving a system of linear equations:

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

Let’s solve it step by step.

Step 1: Solve one equation for one variable

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

Step 2: Substitute into the second equation

Substitute $x = 5 - y$ into $x - 2y = -4$: $(5 - y) - 2y = -4$ Simplify: $5 - 3y = -4$ $-3y = -4 - 5$ $-3y = -9$ $y = 3$

Step 3: Solve for $x$

Substitute $y = 3$ into $x = 5 - y$: $x = 5 - 3$ $x = 2$

Solution:

The solution is: $x = 2, \, y = 3$

Verification:

1. Substitute into $x + y = 5$: $2 + 3 = 5 \, \text{(True)}$
2. Substitute into $x - 2y = -4$: $2 - 2(3) = -4 \, \text{(True)}$

The solution satisfies both equations. The answer is: $\boxed{(2, 3)}$

Do you have any questions, or would you like a graph of the solution?

5 Related Questions:

1. How can you graphically represent the solution of a system of linear equations?
2. What are other methods to solve a system of equations, such as substitution or elimination?
3. What does it mean if a system of equations has no solution or infinitely many solutions?
4. How do you check your solution if the system of equations involves fractions or decimals?
5. What are some real-world applications of solving systems of linear equations?

Tip:

Always verify your solution by substituting it back into the original equations to ensure accuracy.