Question

Given, $x=12$ and $3x=4y^2$
In the system of equations above, if $y>0$, what is the value of $x^{2}y$ ?

• A. $36$
• B. $108$
• C. $432$
• D. $1296$

Answer 1

Answer: (C)

$432$

Substitute $x=12$ in $3x=4y^2$ as shown below:

$3\left(12\right)=4y^2$

$\Rightarrow 36=4y^2$

$\Rightarrow \frac{36}{4}=\frac{4y^2}{4}$

$\Rightarrow 9=y^2$

Either $y=3$ or $y=-3$, but since it is given that $y>0$,

Therefore, $y=3$.

Now, $x^{2}y=\left(12{)}^2\right(3)=144(3)=432$.

Hence, option C is correct.