the sum is 9 and the difference is 4

Answer 1

I am assuming we are talking about the sum and difference of two numbers which I will call 'a' and 'b'.

The statement can be written as:

a + b = 9

a - b = 4

There are a few ways to solve this system of equations. One way is to solve for the same unknown in each, namely:

a + b = 9 | - b

a = 9 - b

for the first equation, and:

a - b = 4 | + b

a = 4 + b

for the second. Now we can equate the a's and get:

9 - b = a = 4 + b

9 - b = 4 + b | + b

9 = 4 + 2b | - 4

9 - 4 = 2b

2b = 5

b = 2.5

Now we can use the value for 'b' to determine the value for 'a' using, e.g. a = 4 + b:

a = 4 + b = 4 + 2.5 = 6.5

The two numbers are: 2.5 and 6.5.