The sum of two numbers is 30 and their difference is 2. Find the two numbers by writing and solving a system of equations.
x+y = 30
x-y = 2
add them
2x = 32
x = 16
then, mentally, y = 14
check:
16+14 = 30
16-14 = 2 , yeahhh!
To find the two numbers, let's first assign variables to them. Let's call the two numbers x and y.
The first condition given is that the sum of the two numbers is 30. We can write this as an equation:
x + y = 30 ...(Equation 1)
The second condition given is that the difference between the two numbers is 2. We can write this as another equation:
x - y = 2 ...(Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of elimination.
We can eliminate one variable by subtracting Equation 2 from Equation 1.
(x + y) - (x - y) = 30 - 2
Simplifying this equation, we get:
x + y - x + y = 28
2y = 28
Dividing both sides by 2:
y = 14
Now that we have found the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use Equation 1:
x + 14 = 30
Subtracting 14 from both sides:
x = 16
Therefore, the two numbers are 16 and 14.