SOLUTION: 4x - 2y= 2 +x 8y -7x = -2y -2x using the system of equations above, what is the average of x and y?

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: 4x - 2y= 2 +x 8y -7x = -2y -2x using the system of equations above, what is the average of x and y?      Log On


   

Question 1097059: 4x - 2y= 2 +x
8y -7x = -2y -2x
using the system of equations above, what is the average of x and y?
Found 2 solutions by amalm06, josh_jordan:
Answer by amalm06(224) About Me  (Show Source):
You can put this solution on YOUR website!
4x-2y=2+x
8y-7x=-2y-2x
3x-2y=2
-5x+10y=0 so 10y=5x so x=2y
8y-2y=2+2y
4y=2 so y=1/2
Therefore, x = 1
Average=(1+0.5)/2=3/4 (Answer)

Answer by josh_jordan(263) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's rewrite each equation so they will both be in the same order and in standard form:

4x - 2y = 2 + x =====> 3x - 2y = 2

8y - 7x = -2y - 2x =====> -5x + 10y = 0

We now have

3x - 2y = 2
-5x + 10y = 0

Multiply the first equation by 5, giving us:

15x - 10y = 10
-5x + 10y = 0

We can now add equation 1 to equation 2, giving us

10x = 10

Dividing both sides of the equation by 10 will give us our x value:

x = 1

Now replace x with 1 in equation 1:

3(1) - 2y = 2 =====> 3 - 2y = 2 =====> -2y = -1 =====> y = 1/2

We now have our x and y values: x = 1 and y = 1/2

We are asked to find the average of x and y. To find the average of 2 numbers, add both numbers together and divide that result by 2. So, in our case:

1 + 1/2 = 1.5 =====> 1.5 / 2 =====> 0.75 or 3/4

Answer: 0.75 or 3/4