9x+3y=24. x-3y=-14 solve it it substitution method

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

1. **Rewrite one of the equations to express one variable in terms of the other.**

   Let's take the second equation and solve for \( x \):

   \[
   x - 3y = -14
   \]

   Add \( 3y \) to both sides:

   \[
   x = 3y - 14
   \]

2. **Substitute this expression into the first equation.**

   Now, substitute \( x = 3y - 14 \) into the first equation:

   \[
   9x + 3y = 24
   \]

   Replace \( x \) with \( 3y - 14 \):

   \[
   9(3y - 14) + 3y = 24
   \]

3. **Simplify and solve for \( y \).**

   Distribute the 9:

   \[
   27y - 126 + 3y = 24
   \]

   Combine like terms:

   \[
   30y - 126 = 24
   \]

   Add 126 to both sides:

   \[
   30y = 150
   \]

   Divide by 30:

   \[
   y = 5
   \]

4. **Substitute \( y \) back into the expression for \( x \).**

   Use \( y = 5 \) in the expression \( x = 3y - 14 \):

   \[
   x = 3(5) - 14
   \]

   Simplify:

   \[
   x = 15 - 14
   \]

   \[
   x = 1
   \]

So, the solution to the system of equations is \( x = 1 \) and \( y = 5 \).

### Solution:
\[
x = 1, \quad y = 5
\]

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

### Related Questions:
1. Can you show how to solve the system using the elimination method?
2. How can we verify the solution \( x = 1 \) and \( y = 5 \)?
3. What would the graph of these two equations look like?
4. How do substitution and elimination methods compare in terms of efficiency?
5. How can we set up a system of equations from a word problem?
6. What are the steps for solving a system of equations with three variables?
7. How can we identify if a system of equations has no solution or infinitely many solutions?
8. What are some real-life applications of solving systems of equations?

### Tip:
Always check your solutions by substituting them back into the original equations to ensure they satisfy both equations.

Learn how to solve the system of equations 9x + 3y = 24, x - 3y = -14 using the substitution method with a detailed step-by-step solution. This problem involves key algebraic concepts, including systems of equations and the substitution method. Suitable for high school students.

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