Let's solve the system of equations step by step to find the resulting equation that Kira obtained.
Given the system of equations:
1) [tex]\( 3y = 12x \)[/tex]
2) [tex]\( x^2 + y^2 = 81 \)[/tex]
1. Isolate [tex]\( y \)[/tex] in the first equation:
Starting with the first equation:
[tex]\[ 3y = 12x \][/tex]
Divide both sides by 3 to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{12x}{3} \][/tex]
[tex]\[ y = 4x \][/tex]
2. Substitute [tex]\( y \)[/tex] into the second equation:
Now substitute [tex]\( y = 4x \)[/tex] into the second equation:
[tex]\[ x^2 + y^2 = 81 \][/tex]
Replace [tex]\( y \)[/tex] with [tex]\( 4x \)[/tex]:
[tex]\[ x^2 + (4x)^2 = 81 \][/tex]
Simplify the equation:
[tex]\[ x^2 + 16x^2 = 81 \][/tex]
Combine like terms:
[tex]\[ 17x^2 = 81 \][/tex]
However, before combining like terms, the resulting equation prior to simplification is:
[tex]\[ x^2 + 16x^2 = 81 \][/tex]
Therefore, the resulting equation that Kira obtained is [tex]\(x^2 + 16x^2 = 81\)[/tex].
So, the correct answer is:
A. [tex]\( x^2 + 16x^2 = 81 \)[/tex]
