Select the correct answer.

Which equation combines with the given equation to form a system of equations with the solution *x* = 3 and *y* = 9?

*x* + 2*y* = 21

 **A.** 

4*x* + 6*y* = 64

 **B.** 

2*x* + *y* = 36

 **C.** 

4*x* + *y* = 21

 **D.** 

-3*x* + 4*y* = 33

 **E.** 

3*x* + 2*y* = 28

To determine which equation combines with \(x + 2y = 21\) to form a system of equations with the solution \(x = 3\) and \(y = 9\), we can substitute these values into each option and see if the resulting equation holds true.

1. **Given Equation**: 
   \[
   x + 2y = 21
   \]
   Substituting \(x = 3\) and \(y = 9\):
   \[
   3 + 2(9) = 3 + 18 = 21 \quad \text{(holds true)}
   \]

2. **Check Each Option**:

   **A.** \(4x + 6y = 64\)  
   Substituting:
   \[
   4(3) + 6(9) = 12 + 54 = 66 \quad \text{(not true)}
   \]

   **B.** \(2x + y = 36\)  
   Substituting:
   \[
   2(3) + 9 = 6 + 9 = 15 \quad \text{(not true)}
   \]

   **C.** \(4x + y = 21\)  
   Substituting:
   \[
   4(3) + 9 = 12 + 9 = 21 \quad \text{(holds true)}
   \]

   **D.** \(-3x + 4y = 33\)  
   Substituting:
   \[
   -3(3) + 4(9) = -9 + 36 = 27 \quad \text{(not true)}
   \]

   **E.** \(3x + 2y = 28\)  
   Substituting:
   \[
   3(3) + 2(9) = 9 + 18 = 27 \quad \text{(not true)}
   \]

From the checks above, the correct answer is **C.** \(4x + y = 21\).

If you want further details or have any questions, please let me know. Here are some follow-up questions for deeper understanding:

1. How do you solve systems of equations using substitution?
2. What is the graphical representation of these equations?
3. Can you explain how to verify solutions for systems of equations?
4. What are other methods to solve systems of equations (e.g., elimination)?
5. What would happen if we changed the solution values for \(x\) and \(y\)?

**Tip:** Always check your proposed solutions in both equations to confirm they satisfy the system.

Which equation combines with the given equation to form a system of equations with the solution x = 3 and y = 9? x + 2y = 21

Explore how to determine which equation pairs with x + 2y = 21 to create a system of equations with the solution x = 3 and y = 9. This lesson includes step-by-step checks for each option, highlighting algebraic principles.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation