https://file.aiquickdraw.com/mathbot/file/17267733283069q5umt6z.jpg

The solution to the system of equations is:

\[
x = -2, \quad y = -6, \quad z = -3
\]

Would you like more details or have any questions?

Here are some related questions for further practice:
1. What is the method used to solve a system of equations like this?
2. How can you check if the solution satisfies all three equations?
3. How would the solution change if one of the constants (e.g., 4 in the first equation) were different?
4. Can you solve the system graphically?
5. What happens if the system of equations has no solutions or infinite solutions?

**Tip:** Always substitute the solution back into the original equations to verify its correctness!

Solve the following system of equations for all three variables:
1. 7x - 5y + 4z = 4
2. -10x + 3y - 2z = 8
3. x + 2y - 4z = -2

Learn how to solve a system of three linear equations, including detailed steps for solving for x, y, and z using elimination or substitution methods. This algebra problem is suitable for Grades 10-12.

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