We are given a system of equations to solve by substitution:

$y = 3x - 7$ $2x + 5y = 16$

Step 1: Substitute the expression for $y$ from the first equation into the second equation.

We substitute $y = 3x - 7$ into $2x + 5y = 16$:

$2x + 5(3x - 7) = 16$

Step 2: Simplify and solve for $x$.

First, expand the equation:

$2x + 15x - 35 = 16$

Now combine like terms:

$17x - 35 = 16$

Add 35 to both sides:

$17x = 51$

Now solve for $x$ by dividing both sides by 17:

$x = \frac{51}{17} = 3$

Step 3: Substitute $x = 3$ back into the first equation to find $y$.

Substitute $x = 3$ into $y = 3x - 7$:

$y = 3(3) - 7 = 9 - 7 = 2$

Step 4: Final answer as an ordered pair.

The solution to the system is:

$\boxed{(3, 2)}$

Would you like any further details or clarifications?

Here are some related questions:

1. How can we verify the solution of a system of equations?
2. What are other methods besides substitution to solve a system of equations?
3. What happens when a system has no solution or infinite solutions?
4. How do we graphically interpret the solution to a system of equations?
5. What are some real-life applications of solving systems of equations?

Tip: Substitution is especially effective when one equation is already solved for one variable.