To solve a system using the substitution method, we follow these general steps:

1. Solve one equation for one variable (in terms of the other).
2. Substitute this expression into the other equation.
3. Solve for the remaining variable.
4. Substitute back into the first equation to find the value of the other variable.
5. State the solution as an ordered pair $(x, y)$.

Let's assume you have a system of equations such as:

$\text{Equation 1:} \quad x + 2y = 8$ $\text{Equation 2:} \quad 3x - y = 5$

Step 1: Solve one equation for one variable

Let's solve Equation 1 for $x$:

$x = 8 - 2y$

Step 2: Substitute this expression into Equation 2

Substitute $x = 8 - 2y$ into Equation 2:

$3(8 - 2y) - y = 5$

Step 3: Simplify and solve for $y$

$24 - 6y - y = 5$ $24 - 7y = 5$ $-7y = 5 - 24$ $-7y = -19$ $y = \frac{-19}{-7} = \frac{19}{7}$

Step 4: Substitute $y = \frac{19}{7}$ back into the expression for $x$

Substitute $y = \frac{19}{7}$ into $x = 8 - 2y$:

$x = 8 - 2\left(\frac{19}{7}\right)$ $x = 8 - \frac{38}{7}$ $x = \frac{56}{7} - \frac{38}{7} = \frac{18}{7}$

Step 5: Solution as an ordered pair

The solution to the system is:

$(x, y) = \left( \frac{18}{7}, \frac{19}{7} \right)$

---

Do you need further details on any step, or do you have any questions?

Here are five related questions for you to try:

1. Solve the system: $x - y = 4$ and $2x + 3y = 12$ using substitution.
2. Solve for $x$ and $y$ if $x + 3y = 10$ and $4x - y = 6$.
3. What happens if both equations simplify to the same line when using substitution?
4. Can you apply substitution to the system $2x + 2y = 4$ and $4x + 4y = 8$?
5. How would substitution work if one equation is quadratic in form?

Tip: Always simplify expressions as much as possible before substituting to avoid unnecessary complications.