# Algebra: functions and linear system

Part 1

1. Define the word "function."

2. Give an example of a function using a set of at least 4 ordered pairs. The domain will be any four integers between 0 and +10. The range will be any four integers between -12 and 5.

3. Explain why the example models a function.

4. Give an example of at least four ordered pairs that does not model a function. The domain will be any four integers between 0 and +10. The range will be any four integers between -12 and +5.

5. Explain why your example does not model a function.

Part 2

1. Select any two integers between -12 and +12 which will become solutions to a system of two equations.

2. Write two equations that have your two integers as solutions. Show how using the equations using your integers. Solve the system of equations by the addition/subtraction method. Make sure you the necessary 5 steps are included.

https://brainmass.com/math/number-theory/algebra-functions-linear-system-563861

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Please see attached.

Part 1

1. A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

2. , where A= {2,4,6,8} and B={-8,-6,-4,-2}, f(x) =x-10

3. The model above is a function, because to each point in A corresponds an unique point of B.

4. , where the pairs are: (2,-8),(2,-6),(4,-4) and (6,-2)

5. The model above isnot a function, because the point 2 from A corresponds to two different points of B.

Part 2

1. Select x=0 and y=2

2. Set

Step 1

Firstly we will multiply first equation by 3 and the second one by -2:

Step 2

Now we add the two equations:

-y =-2

Step 3

Now we divide by -2:

Therefore y=2.

Step 4

Now we plug this value into the first equation and get:

2x+2=2

2x=0

X=0

Step 5

So the solution we got is (x,y) =(0,2)

https://brainmass.com/math/number-theory/algebra-functions-linear-system-563861