We are given the following system of equations:

1. $-2x + 16y = 18$
2. $x - 8y = -9$

Step 1: Solve the second equation for $x$:

We begin with the second equation: $x - 8y = -9$ Solving for $x$: $x = 8y - 9$

Step 2: Substitute $x = 8y - 9$ into the first equation:

Now, substitute this expression for $x$ into the first equation: $-2x + 16y = 18$ Substituting $x = 8y - 9$: $-2(8y - 9) + 16y = 18$ Simplifying the equation: $-16y + 18 + 16y = 18$ The terms involving $y$ cancel out, leaving: $18 = 18$ This is a true statement, meaning the system is consistent and there are infinitely many solutions. The value of $y$ is not fixed, and $x$ can be expressed in terms of $y$.

Step 3: Write the general solution:

Since the equation reduces to a true statement, the system has infinitely many solutions, and $x$ can be written as: $x = 8y - 9$ Thus, the general solution is: $(x, y) = (8y - 9, y)$

Final Answer:

The general solution is: $(x, y) = (8y - 9, y)$ where $y$ can be any real number.

Would you like more details on this process or further clarification? Here are a few related questions to explore:

1. How would you solve a system of equations using substitution or elimination?
2. What happens when a system of equations results in a false statement like $0 = 1$?
3. What does it mean for a system to have infinitely many solutions?
4. How do you identify when two equations represent the same line in a system?
5. How do you graphically interpret a system of equations with infinitely many solutions?

Tip: When solving systems of equations, always check if the equations are dependent (leading to infinite solutions) or inconsistent (leading to no solution).