Use the method of substitution to solve the system of linear equations.

Enter your answer as a point. Example: (2,5.5)
Enter each value as a number (like 5, -3, 2.2) or as a calculation (like 5/3, 2^3, 5+4)
Enter no solution for a system with no solutions.
Enter infinitely many for a system with infinitely many solutions.

To solve the system of linear equations using the method of substitution, follow these steps:

1. **Solve one equation for one variable.**
2. **Substitute this expression into the other equation.**
3. **Solve the resulting equation for the other variable.**
4. **Substitute back to find the first variable.**

Let's consider the following example system of equations:

\[
\begin{cases}
2x + 3y = 6 \\
x - y = 4
\end{cases}
\]

### Step 1: Solve one equation for one variable

We solve the second equation for \( x \):

\[ x - y = 4 \]
\[ x = y + 4 \]

### Step 2: Substitute this expression into the other equation

Substitute \( x = y + 4 \) into the first equation:

\[ 2(y + 4) + 3y = 6 \]

### Step 3: Solve the resulting equation for the other variable

Simplify and solve for \( y \):

\[ 2y + 8 + 3y = 6 \]
\[ 5y + 8 = 6 \]
\[ 5y = -2 \]
\[ y = -\frac{2}{5} \]

### Step 4: Substitute back to find the first variable

Substitute \( y = -\frac{2}{5} \) back into \( x = y + 4 \):

\[ x = -\frac{2}{5} + 4 \]
\[ x = -\frac{2}{5} + \frac{20}{5} \]
\[ x = \frac{18}{5} \]

Thus, the solution to the system is:

\[ \left( \frac{18}{5}, -\frac{2}{5} \right) \]

So the solution in the format requested is:

\[
\left( \frac{18}{5}, -\frac{2}{5} \right)
\]

Would you like more details or have any questions about this solution?

Here are 5 questions you might want to ask:
1. Can you explain the substitution method in more detail?
2. How do you check if a system has no solutions?
3. What are some other methods for solving systems of linear equations?
4. How can I verify the solution to a system of linear equations?
5. What does it mean when a system has infinitely many solutions?

**Tip:** When substituting expressions, carefully simplify and solve each step to avoid errors.

Explore how to solve a system of linear equations using the substitution method. Step-by-step solution provided with detailed calculations and examples. Suitable for high school students and anyone studying linear algebra.

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