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To solve the system of equations by substitution, we will proceed as follows:

The system of equations given is:

1. \( y = 3x - 7 \)
2. \( 2x + 5y = 16 \)

### Step 1: Substitute the expression for \( y \) from the first equation into the second equation.
We know that \( y = 3x - 7 \), so substitute this into the second equation:

\[
2x + 5(3x - 7) = 16
\]

### Step 2: Simplify the equation and solve for \( x \).

Distribute the 5:
\[
2x + 15x - 35 = 16
\]

Combine like terms:
\[
17x - 35 = 16
\]

Add 35 to both sides:
\[
17x = 51
\]

Divide by 17:
\[
x = 3
\]

### Step 3: Substitute \( x = 3 \) back into the first equation to solve for \( y \).
Using the first equation \( y = 3x - 7 \):

\[
y = 3(3) - 7 = 9 - 7 = 2
\]

### Solution:
The solution to the system is the ordered pair \( (3, 2) \).

Would you like any further clarification or details?

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Here are 5 related questions to expand your understanding:

1. How can substitution be used to solve non-linear systems of equations?
2. What are the advantages of using substitution compared to other methods like elimination?
3. How would you solve this system graphically and compare the result?
4. Can you apply substitution to a system of three equations with three variables?
5. What happens if there are infinitely many solutions to the system?

**Tip:** Always check your solution by substituting both values back into the original equations to verify they satisfy both.

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

Learn how to solve the system of equations using substitution: y = 3x - 7 and 2x + 5y = 16. Follow a step-by-step guide to understand how to substitute and simplify the equations. Suitable for students in Grades 9-11.

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