Two numbers have a product that is 10 less than their sum. If the smaller number is 6 less than the bigger number, what are the two numbers

Answer 1

Let x= first number (bigger number)

Let y= second number (smaller number)

Two numbers have a product that is 10 less than their sum: xy=x+y-10

Smaller number is 6 less than the bigger number: x-6=y

Plug in (x-6) for y:

x(x-6)=x+(x-6) -10

Simplify the equation so that it one side equals 0

x² - 6x= x+x-6-10

x²-6x= 2x-16

x²-6x-2x+16= 0

x²-8x+16= 0

Find the binomials by trying out multiples of 16, (±1,±2,±4,±8,±16)

(x-4)(x-4)=0

x=4

Plug in 4 for x to find the value of y

x-6=y

4-6=y

-2=y

Check your answer by plugging in x and y:

xy=x+y-10

4(-2)=4+ -2 -10

-8=2-10

-8=-8

x=4, y=-2