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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 solve this problem, let's analyze each option by substituting \( x = 3 \) and \( y = 9 \) into each equation to see which one satisfies the equation along with the given equation \( x + 2y = 21 \).

### Given equation:
The equation provided is:
\[
x + 2y = 21
\]
Substituting \( x = 3 \) and \( y = 9 \):
\[
3 + 2(9) = 3 + 18 = 21
\]
This is correct, so we proceed to check each option.

### Option A: \( 4x + 6y = 64 \)
Substitute \( x = 3 \) and \( y = 9 \):
\[
4(3) + 6(9) = 12 + 54 = 66 \neq 64
\]
This does not satisfy the equation, so **A is incorrect**.

### Option B: \( 2x + y = 36 \)
Substitute \( x = 3 \) and \( y = 9 \):
\[
2(3) + 9 = 6 + 9 = 15 \neq 36
\]
This does not satisfy the equation, so **B is incorrect**.

### Option C: \( 4

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 + 2y = 21

 A. 4x + 6y = 64
 B. 2x + y = 36
 C. 4x + y = 21
 D. -3x + 4y = 33
 E. 3x + 2y = 28

Learn how to solve a system of equations by verifying which equation combines with x + 2y = 21 to produce a system with the solution x = 3 and y = 9. This problem covers essential concepts in algebra, focusing on substitution and systems of equations, suitable for students in Grades 8-10.

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