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=…

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asked Oct 22, 2017 122k views

2 Answers

Marco Roy · Answer 1 · 2017-10-26T02:18:14+0000

Answer:

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 →
$x=\pm4$ ,
$y=\pm8$