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'.
\(\Rightarrow x=\frac{1}{2}y\)
Situation 2 - 'The product of two numbers is 32'
\(\Rightarrow x\times y=xy=32\)
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
\(xy=32\)
\(\frac{1}{2}y\times y=32\)
\(y^2=64\)
\(y=\pm8\)
put value of y in x,
\(x=\frac{1}{2}\times(\pm8)\)
\(x=\pm4\)
Values are → \(x=\pm4\) , \(y=\pm8\)
