Answer:
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)
