The image contains a system of linear equations being solved using the elimination method. Let's go through the process shown:

Given Equations:

1. $2x + 3y = 16$
2. $4x + 5y = 20$

Elimination Method:

Step 1: Multiply the first equation by 2 to align the coefficients of $x$:

$2(2x + 3y = 16) \Rightarrow 4x + 6y = 32$

Step 2: Subtract the second equation from this modified first equation:

$(4x + 6y = 32) - (4x + 5y = 20)$ $(4x - 4x) + (6y - 5y) = 32 - 20$ $0x + y = 12$ $y = 12$

Step 3: Substitute $y = 12$ into one of the original equations (e.g., $2x + 3y = 16$) to solve for $x$:

$2x + 3(12) = 16$ $2x + 36 = 16$ $2x = 16 - 36$ $2x = -20$ $x = -10$

Final Solution:

$x = -10, \quad y = 12$

This solution is derived correctly from the elimination steps shown. Do you want to go through more details on any step?

Here are 5 related questions:

1. How does the elimination method differ from the substitution method?
2. Can elimination always be used for any system of linear equations?
3. What happens if the system of equations is dependent or inconsistent?
4. How would you approach solving the system using matrices?
5. What are the advantages of using elimination over graphing the system?

Tip: Always check the solution by substituting both values back into the original equations to ensure correctness.