The sum of a certain number and a second number is -42. The difference of the first number and the second number is 52. Find the number?

Let the first number be x, and the second number be y. So,

x + y = -42

x - y = 52 add the equations;

2x = 10 divide by 2 both sides;

x = 5 substitute 5 for x into the first equation;

5 + y = -42 subtract 5 to both sides;

y = - 47

So the numbers are 5 and -47.

Check:

5 + (-47) = -42

5 - (-47) = 5 + 47 = 52.