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 system of equations. x y equals 32. x equals StartFraction one-half EndFraction y.
A system of equations. x y equals 32. x equals y minus StartFraction one-half EndFraction.
A system of equations. x plus y equals 32. x equals y minus StartFraction one-half EndFraction.
A system of equations. x plus y equals 32. x equals StartFraction one-half EndFraction y.

Answer 1

The first option.

System:
x·y = 32
x = (1/2) y

Solving: (1/2) y·y = 32 → (1/2) y^2 = 32 → y^2 = 64 → y = ±8. Then x = (1/2) y = ±4.