We are tasked with solving the following system of linear equations:

1. $5x - 4y = 16$
2. $x + 4y = 32$

Step 1: Solve the second equation for $x$

From $x + 4y = 32$: $x = 32 - 4y$

Step 2: Substitute $x = 32 - 4y$ into the first equation

Substitute into $5x - 4y = 16$: $5(32 - 4y) - 4y = 16$ Simplify: $160 - 20y - 4y = 16$ $160 - 24y = 16$ $-24y = 16 - 160$ $-24y = -144$ $y = 6$

Step 3: Substitute $y = 6$ into $x = 32 - 4y$

$x = 32 - 4(6)$ $x = 32 - 24$ $x = 8$

Final Solution:

$x = 8, \; y = 6$

Would you like me to verify or explain any step further? Let me know if you want additional practice or have related questions!

Related Questions:

1. How do you solve systems of linear equations graphically?
2. What is substitution, and when is it most effective in solving equations?
3. Can you explain elimination as an alternative to solve systems of equations?
4. How do you write a real-world problem modeled by these equations?
5. What happens when two linear equations in a system are parallel or the same line?

Tip:

Always double-check your solution by substituting $x$ and $y$ back into the original equations.