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Which equation combines with the given equation to form a system of equations with the solution [tex]$x=3$[/tex] and [tex]$y=9$[/tex]?

Given equation: [tex]$x + 2y = 21$[/tex]

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

Sagot :

GinnyAnswer
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.
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