Question

the point (3, 4) in the xy - plane is a solution to which of the following systems of inequalities?
a (x>0) (y > 0)
b (x>0) (y < 0)
c (x<0) (y > 0)
d (x<0) (y < 0)

Explanation:

Step1: Analyze the x - value

For the point $(3,4)$, the x - coordinate is $x = 3$. Since $3>0$, we need to find an option where the x - inequality allows $x>0$.

Step2: Analyze the y - value

The y - coordinate of the point $(3,4)$ is $y = 4$. Since $4>0$, we need to find an option where the y - inequality allows $y>0$.

Step3: Check each option

• Option A: $x>0$ and $y>0$. For $x = 3$ and $y = 4$, $3>0$ and $4>0$, so the point $(3,4)$ satisfies this system.
• Option B: $x>0$ and $y<0$. Since $y = 4>0$, the point $(3,4)$ does not satisfy this system.
• Option C: $x<0$ and $y>0$. Since $x = 3>0$, the point $(3,4)$ does not satisfy this system.
• Option D: $x<0$ and $y<0$. Since $x = 3>0$ and $y = 4>0$, the point $(3,4)$ does not satisfy this system.

Answer:

A. $x > 0$, $y > 0$