Answer:
The numbers are 30 and -10.
Explanation:
The sum of two numbers is 20 (addition)
x + y = 20
The difference is 40 (subtraction)
x - y = 40
To solve an equation, you can only have one variable. Solve one of these for a variable (it doesn't matter which one).
x - y = 40 Add y to both sides
x = 40 + y
Now you have a new value for x (40 + y), so you can plug it into your other equation.
x + y = 20 Plug in (40 + y) for x
40 + y + y = 20 Combine like terms (y + y)
40 + 2y = 20 Subtract 40 from both sides
2y = -20 Divide both sides by 2
y = -10
Now, plug your y into either equation.
x + y = 20 Plug in -10 for y
x + (-10) = 20 Simplify
x - 10 = 20 Add 10 to both sides
x = 30
Check your work by plugging these numbers into both equations.
x + y = 20 Plug in
30 + (-10) = 20 Simplify
30 - 10 = 20 Simplify
20 = 20
and
x - y = 40 Plug in
30 - (-10) = 40 Simplify
30 + 10 = 40
40 = 40