To solve this system of linear equations using substitution, we will follow these steps:

Equations:

1. $x - y = -8$
2. $7x + 5y = 16$

Step 1: Solve one equation for one variable

From equation (1), solve for $x$ in terms of $y$: $x = y - 8$

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

Substitute $x = y - 8$ into equation (2): $7x + 5y = 16$ $7(y - 8) + 5y = 16$

Simplify: $7y - 56 + 5y = 16$ $12y - 56 = 16$

Step 3: Solve for $y$

$12y = 72$ $y = 6$

Step 4: Substitute $y = 6$ into $x = y - 8$

$x = 6 - 8$ $x = -2$

Final Answer:

The solution to the system is: $x = -2, \; y = 6$

Would you like a detailed explanation of each step? Let me know!

Related Questions:

1. What is the elimination method, and how does it compare to substitution?
2. How can this solution be checked for accuracy?
3. Can you graph the system of equations to verify the solution visually?
4. How does substitution work for nonlinear systems of equations?
5. What happens when a system of equations has no solution or infinitely many solutions?

Tip:

Always substitute the solution back into both original equations to verify accuracy!