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

Answer:There are 2 sets of numbers that work...x = 3, y = 5and x = 6, y = 2Step-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 + 10now 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)sox - 6 =  0  becomes   x = 6    (add 6 to both sides)andx - 3 = 0  becomes x = 3      (add 3 to both sidesIf 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)