Solve this equation:
1.x-3y = -9
2x+7y=8
The theorem is:
Solving system of linear equations by substitution method 

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

### Given system of equations:
1. \( x - 3y = -9 \)
2. \( 2x + 7y = 8 \)

### Step 1: Solve one equation for one variable
Let's solve the first equation for \( x \) in terms of \( y \).

\[
x - 3y = -9
\]

Add \( 3y \) to both sides:

\[
x = 3y - 9
\]

### Step 2: Substitute the expression for \( x \) into the second equation
Now substitute \( x = 3y - 9 \) into the second equation:

\[
2x + 7y = 8
\]

Substitute \( x \):

\[
2(3y - 9) + 7y = 8
\]

### Step 3: Solve for \( y \)
Expand the equation:

\[
6y - 18 + 7y = 8
\]

Combine like terms:

\[
13y - 18 = 8
\]

Add 18 to both sides:

\[
13y = 26
\]

Now divide by 13:

\[
y = 2
\]

### Step 4: Substitute \( y = 2 \) back into the expression for \( x \)
Substitute \( y = 2 \) into \( x = 3y - 9 \):

\[
x = 3(2) - 9 = 6 - 9 = -3
\]

### Step 5: Solution
The solution to the system is:

\[
x = -3, \quad y = 2
\]

### Final Answer:
The solution to the system of equations is \( x = -3 \) and \( y = 2 \).

---

Do you want further details or have any questions?

Here are 5 related questions to explore:
1. How can we verify if \( x = -3 \) and \( y = 2 \) satisfy the original equations?
2. How would you solve this system using the elimination method?
3. What are some real-world applications of solving systems of linear equations?
4. Can a system of linear equations have no solution? How do you know?
5. What is the difference between consistent, inconsistent, and dependent systems of equations?

**Tip:** When using substitution, always simplify expressions carefully before substituting values back into other equations.

Solve this equation: 1. x - 3y = -9, 2. 2x + 7y = 8. The theorem is: Solving system of linear equations by substitution method

Learn how to solve the system of linear equations x - 3y = -9 and 2x + 7y = 8 using the substitution method. This solution covers key algebraic concepts and provides a detailed step-by-step guide. Suitable for students in Grades 8-10.

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