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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.

Solve the system of equations by substitution: y = 3x - 7 and 2x + 5y = 16.

Learn how to solve the system of linear equations y = 3x - 7 and 2x + 5y = 16 using the substitution method. This step-by-step solution covers algebraic concepts, including substitution and solving linear equations. Suitable for students in Grades 8-10.

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