To solve this system of linear equations by substitution, we have the equations:

1. $x = 17 - 4y$
2. $y = x - 2$

We can substitute the expression for $x$ from the first equation into the second equation:

Step-by-Step Solution

1. Substitute $x = 17 - 4y$ into the second equation: $y = (17 - 4y) - 2$

2. Simplify the right side of the equation: $y = 17 - 4y - 2$ $y = 15 - 4y$

3. Add $4y$ to both sides to get all terms involving $y$ on one side: $y + 4y = 15$ $5y = 15$

4. Divide both sides by 5: $y = 3$

5. Substitute $y = 3$ back into the first equation to find $x$: $x = 17 - 4(3)$ $x = 17 - 12$ $x = 5$

Solution

The solution to the system is: $(x, y) = (5, 3)$

Would you like a detailed explanation of each step, or do you have any questions?

Here are some related questions for further exploration:

1. How would the solution change if we used a different method, such as elimination?
2. Can we verify the solution by substituting $x$ and $y$ back into both original equations?
3. What are the implications of having only one solution in a system of linear equations?
4. How does substitution compare to graphing when solving systems of equations?
5. Are there any scenarios where substitution is not the best method to use?

Tip: Always double-check your solution by substituting the values back into the original equations to ensure they satisfy both.