The sum of two numbers is 19 and their difference is 5. What are the two numbers?
2 answers:
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<u>ANSWER</u>
<u>EXPLANATION</u>
To find the value of a function, f(x) at a given value x=a, we plug in x=a into f(x) to obtain f(a) in simplified form.
The first function is
To find f(7), we substitute x=7, into the function.
The second function is
To find f(4), we replace x with 4 to obtain,
2 numbers can be represented by the variables x and y.
Set up a system of equations:
The two numbers added together will result in a sum of 33. However, one number subtracted from another will result in a difference of 1.
In both systems of equations, there are inverses of variable y. Therefore, we can combine the systems of equations by adding them together:
Divide both sides by 2 to get x by itself:
One of the numbers will be 17.
Plug the value into one of the equations:
Add y to both sides:
Subtract both sides by 1 to get y by itself:
The two numbers that sum up to 33, with a difference of 1 between them, will be 16 and 17.