Question

The product of two numbers is 32. The first number, x, is one-half of the second number, y. Which system of equations can be used to find the two numbers? A. xy=32 x=1/2y B. xy=32 x=y-1/2 C. x+y=32 x=y-1/2 Dxty=32 x=1/2y

Answer 1

A

Explanation:

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Answer 2

Option A - xy=32, x=1/2y

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=(1)/(2)y`

Situation 2 - 'The product of two numbers is 32'

`\Rightarrow x* 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`

`(1)/(2)y* y=32`

`y^2=64`

`y=\pm8`

put value of y in x,

`x=(1)/(2)*(\pm8)`

`x=\pm4`

Values are →
`x=\pm4` ,
`y=\pm8`