The system of equations provided in the image is:

1. $y = x + 8$
2. $4x - 2y = -12$

Solving the system of equations:

Step 1: Substitute $y = x + 8$ into the second equation.

The second equation is: $4x - 2y = -12$ Substitute $y = x + 8$: $4x - 2(x + 8) = -12$

Step 2: Simplify the equation.

$4x - 2x - 16 = -12$ $2x - 16 = -12$

Step 3: Solve for $x$.

$2x = -12 + 16$ $2x = 4$ $x = 2$

Step 4: Solve for $y$ using $y = x + 8$.

$y = 2 + 8$ $y = 10$

Solution:

The solution to the system of equations is: $x = 2, \, y = 10$

Would you like me to explain this process in more detail or explore another method?

Follow-Up Questions:

1. What method would you like to use next, such as elimination or graphing?
2. Would you like a verification of the solution by substituting back into both equations?
3. How does substitution compare to elimination for solving systems of equations?
4. Can you extend this to solve three-variable systems?
5. Would you like a visual graph representation of the solution?

Tip:

When solving systems of equations, substitution is particularly useful when one equation is already solved for one variable.