Two positive numbers have a sum of 8 and their product is equal to the larger number plus 10

There are 2 sets of numbers that work ...

x = 3, y = 5

and

x = 6, y = 2

Step-by-step explanation:

Let x be one number, and let y be the other number. We have 2 equations ...

x + y = 8 (two positive numbers have a sum of 8)

xy = y + 10 (their product is equal to the larger number plus 10)

solve the first equation for y, and substitute that into the second equation ...

y = 8 - x

x (8 - x) = 8 - x + 10

now solve for x ...

8x - x² = 18 - x

This is a quadratic, so get everything to one side so it's equal to zero ...

-x² + 9x - 18 = 0 (add x and subtract 18 from both sides)

Now solve for x ...

x² - 9x + 18 = 0 (divide both sides by - 1)

(x - 6) (x - 3) = 0 (factor)

so

x - 6 = 0 becomes x = 6 (add 6 to both sides)

and

x - 3 = 0 becomes x = 3 (add 3 to both sides

If x is 3, then y = 5 (3 + 5 is 8, and 3 (5) = 5 + 10, both equations hold up)

If x is 6, then y = 2 (6 + 2 is 8, and 6 (2) = 2 + 10, both equation hold up)