Answer:
Option A - xy=32, x=1/2y
Step-by-step explanation:
Given : The product of two numbers is 32. The first number, x, is one-half of the second number, y.
To find : Which system of equations can be used to find the two numbers.
Solution: Since, first number =x and second number = y
Situation 1 - 'The first number, x, is one-half of the second number, y'.
[tex]\Rightarrow x=\frac{1}{2}y[/tex]
Situation 2 - 'The product of two numbers is 32'
[tex]\Rightarrow x\times y=xy=32[/tex]
The above two situation matches with Option A.
Therefore, Option A is correct → xy=32 x=1/2y
Solving Situation 1 and 2 we get,
Put x value in situation 2
[tex]xy=32[/tex]
[tex]\frac{1}{2}y\times y=32[/tex]
[tex]y^2=64[/tex]
[tex]y=\pm8[/tex]
put value of y in x,
[tex]x=\frac{1}{2}\times(\pm8)[/tex]
[tex]x=\pm4[/tex]
Values are → [tex]x=\pm4[/tex] , [tex]y=\pm8[/tex]
