To solve the system of equations:

$x + y = 10 \quad \text{(1)}$ $4x + 3y = 18 \quad \text{(2)}$

We can solve this system using substitution or elimination. I will use substitution here.

Step 1: Solve for $x$ in terms of $y$ from equation (1):

$x = 10 - y \quad \text{(3)}$

Step 2: Substitute $x = 10 - y$ into equation (2):

$4(10 - y) + 3y = 18$

Step 3: Expand and simplify:

$40 - 4y + 3y = 18$ $40 - y = 18$

Step 4: Solve for $y$:

$-y = 18 - 40$ $-y = -22$ $y = 22$

Step 5: Substitute $y = 22$ back into equation (3) to find $x$:

$x = 10 - 22$ $x = -12$

Solution:

The solution to the system is $x = -12$ and $y = 22$, which corresponds to the point $(-12, 22)$.

Thus, the correct answer is:

$\boxed{(-12, 22)}$

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

Here are 5 related questions:

1. How can you solve this system using the elimination method?
2. What are the general steps for solving any system of linear equations?
3. Can this method be used for systems with more than two equations?
4. How can you verify if the solution $(-12, 22)$ is correct?
5. What happens if two lines in a system are parallel?

Tip: Substitution is especially useful when one variable is already isolated or can be easily solved for.