# Given $(x+3)(y−4)=0$, what is the relationship between $xy$ and $-12$?

Given

$(x+3)(y−4)=0$

Quantity $A = xy$

Quantity $B = -12$

A Quantity $A$ is greater.
B Quantity $B$ is greater.
C The two quantities are equal.
D The relationship cannot be determined from the information given.

How is the answer D and not C ?

• You are given an equation on the form $ab = 0$. This requires $a = 0$ or $b = 0$. – Andrew Thompson Aug 12 '14 at 9:19

$(x+3)(y-4)=0 ...(I)\Rightarrow$ either $x=-3$ OR $y=4$ OR $x=-3$ AND $y=4$.

If $x=-3$, then $y$ can assume any value and when $y=4$, $x$ can assume any value to satisfy eqn (I)

In both the cases $A=xy$ can be anything, so we can not be sure about $A$ being greater than or less than -$12$.

Only when $x=-3$ AND also, $y=4$, we get $A=-12$, but such condition is not specified in the problem.

Because the first equation says either $x=-3$ or $y=4$ or both and only in last case C is correct.

for example

$$\begin{cases} x=-3\\y=0\end{cases}\rightarrow \begin{cases} A=0\\B=-12\end{cases}$$