We have a system of two linear equations to solve:

1. $3x + 7y = 9$
2. $x + 7y = 17$

Step 1: Subtract the equations

To eliminate $y$, subtract the second equation from the first equation: $(3x + 7y) - (x + 7y) = 9 - 17$ Simplify: $3x - x = -8$ $2x = -8$

Step 2: Solve for $x$

Divide both sides by 2: $x = -4$

Step 3: Substitute $x = -4$ into the second equation

Substitute $x = -4$ into $x + 7y = 17$: $-4 + 7y = 17$ Add 4 to both sides: $7y = 21$ Divide by 7: $y = 3$

Final Solution:

The solution to the system is: $x = -4, \; y = 3$

Would you like me to verify the solution or explain further steps?

---

Questions for deeper understanding:

1. What is the importance of elimination or substitution methods in solving systems of equations?
2. How would the solution change if the coefficients of $y$ were different in the two equations?
3. Can you graphically interpret the solution of this system of equations?
4. How does substitution compare to elimination in terms of efficiency for solving this problem?
5. How can you extend this method to systems with three equations and three variables?

Tip: Always check your solution by substituting the values of $x$ and $y$ back into the original equations to verify accuracy.