the sum of two numbers is 24 and their difference is 2 what are the numbers

Answer 1

Let x be one number and y be the other number, then make two equations based on what was given:

x times y = 24 and x minus y = 2 or:

xy = 24

x - y = 2

There are several ways of solving these two equations together but an easy way is add y to both sides of the second equation to get x = y + 2 then plug "y + 2" into the first equation in place of x to get:

(y + 2)y = 24. Multiply this out to get y² + 2y = 24. Subtract 24 from both sides to get:

y² + 2y - 24 = 0

You can solve this quadratic by factoring:

(y + 6)(y - 4) = 0 then set each part equal to 0

y + 6 = 0 and y - 4 = 0

Solve for y to get two possible values of y.

Plug each of those values of y back into the x = y + 2 equation to get corresponding values of x. You'll get two answers, one where x and y are positive numbers and one where they are negative numbers, Both choices will work as solutions to the problem.