Solve the system by using the substitution method.{(*x*, *y*)} = {(  ,  )}

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.

Solve the system by using the substitution method.

Learn how to solve a system of linear equations using the substitution method. This step-by-step guide demonstrates solving two equations: x + 2y = 8 and 3x - y = 5. Ideal for Grades 8-10, covering core algebraic concepts.

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