The product of a number and 8 less than the number is 65. find the number

Option A (-1, -6)

Option C (10, 49)

Step-by-step explanation:

Two equations are given as y = (x - 2)² - 15 (1)

and -5x + y = -1

y = -1 + 5x (2)

We put the value of y from equation 1 in equation 2.

(x -2)² - 15 = 5x - 1

x² + 4 - 4x - 15 = 5x - 1

x²- 4x - 11 = 5x - 1

x² - 4x - 11 - 5x + 1 = 0

x² - 9x - 10 = 0

x² - 10x + x - 10 = 0

x(x - 10) + 1(x - 10) = 0

(x + 1)(x - 10) = 0

x = -1 , 10

Now we put the value of x in equation 2

y = 5(-1) - 1

y = -5 -1 = -6

For x = 10

y = 5×10 - 1 = 50 - 1 = 49

So solutions are (-1, -6) and (10, 49)

First solution is Option A. (-1, -6) and second solution is Option C.(10, 49)