Certainly! Let's analyze each given equation and verify which one is consistent with the solution [tex]\( x = 3 \)[/tex] and [tex]\( y = 9 \)[/tex].
We are given the first equation:
[tex]\[ x + 2y = 21 \][/tex]
Let's substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = 9 \)[/tex] into each of the options to see which one holds true:
Option A: [tex]\( 4x + 6y = 64 \)[/tex]
[tex]\[ 4(3) + 6(9) = 12 + 54 = 66 \][/tex]
This does not equal 64, hence Option A is incorrect.
Option B: [tex]\( 2x + y = 36 \)[/tex]
[tex]\[ 2(3) + 9 = 6 + 9 = 15 \][/tex]
This does not equal 36, so Option B is incorrect.
Option C: [tex]\( 4x + y = 21 \)[/tex]
[tex]\[ 4(3) + 9 = 12 + 9 = 21 \][/tex]
This is equal to 21, so Option C is correct.
Option D: [tex]\( -3x + 4y = 33 \)[/tex]
[tex]\[ -3(3) + 4(9) = -9 + 36 = 27 \][/tex]
This does not equal 33, making Option D incorrect.
Option E: [tex]\( 3x + 2y = 28 \)[/tex]
[tex]\[ 3(3) + 2(9) = 9 + 18 = 27 \][/tex]
This does not equal 28, making Option E incorrect.
Thus, the correct equation that, combined with [tex]\( x + 2y = 21 \)[/tex], forms a system of equations where [tex]\( x = 3 \)[/tex] and [tex]\( y = 9 \)[/tex] is:
[tex]\[ \boxed{4x + y = 21} \][/tex]
So, the correct answer is Option C.
