Question: One number is 3 more than 2 times another. Their product is 27. Find the numbers. Answer in the form of paired points with the lowest of the two numbers first.
Let the two numbers be x and y.
One number is 3 more than 2 times another. Therefore x = 2y + 3
Their product is 27. Therefore xy = 27
Substituting for x = 2y + 3 into the product equation,
(2y + 3)y = 27
2y^2 + 3y - 27 = 0
(2y + 9)(y - 3) = 0
Hence y = -4.5, or y = 3, giving x = -6, or x = 9
As paired points, the two numbers are: (-4.5, -6) or (3, 9)