SOLUTION: BEEHIVE.... A farmer is tracking two wild honey bees in his field. He maps the first bee's path to the hive on the line 7y = 9x The second bee's path follows the line y = -

Question 182272: BEEHIVE.... A farmer is tracking two wild honey bees in his field. He maps the first bee's path to the hive on the line 7y = 9x
The second bee's path follows the line y = -3x + 12. Their paths cross at the hive. At what coordinates will the farmer find the hive?

I think that I should try to line the variables up on one side, then add one set of variables together and also the integers and then solve for that respective variable. After solving for that variable, I can plug it back into one the two line equations and then find the other variable. The two variable points I get are where the bees' paths intersect?

I made 7y=9x----> 7y-9x=0
I made y=-3x+12----> y+3x=12

I then added the x's together and get -6x=12...solving by division for x, I get x=-2
plugging -2 for x back into the second equation I get y=18 but this does not work at all for the top equation!
Where have I gone wrong or what do I need to do differently????
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A farmer is tracking two wild honey bees in his field. He maps the first bee's path to the hive on the line 7y = 9x
The second bee's path follows the line y = -3x + 12. Their paths cross at the hive. At what coordinates will the farmer find the hive?
------------------------
I think that I should try to line the variables up on one side, then add one set of variables together and also the integers and then solve for that respective variable. After solving for that variable, I can plug it back into one the two line equations and then find the other variable. The two variable points I get are where the bees' paths intersect?
I made 7y=9x----> 7y-9x=0 --> 9x-7y = 0
I made y=-3x+12----> y+3x=12
I then added the x's together and get -6x=12...solving by division for x, I get x=-2
-------------
You can't add the x's and leave out the y's. You should get 8y-6x = 12, but that doesn't help solve the problem.
-----------------
If you want to take that approach, multiply one or both eqns to get the same coefficient for one of the variables.
3x+y = 12 times 3 -->
9x+3y = 36
9x-7y = 0
-------------- Subtract to eliminate x
0x+10y = 36
y = 3.6
Then sub into any eqn and find x
7y=9x Take the simplest one
7*3.6 = 9x
x = 2.8
The point is (2.8,3.6)
--------------------------

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

Find the simultaneous solution like this:
(1)
(2)
multiply both sides of (2) by
and add the equations
(1)
(2)

Now plug this result back into either (1) or (2)

Multiply both sides by

The hive is at (14/5,18/5)
check answers:
(1)
(1)

and
(2)
(2)

The crossing looks about right
RELATED QUESTIONS
Two bees have each found a food source. The first bee's path back to the hive follows the (answered by Mathtut)
A canoeist rows downstream in 1.5 hours and back upstream in 3 hours. What is the rate of (answered by mananth)
as many as 60,000 bees can live in a 3 cubic feet of space.there are about 360,000 bees... (answered by Theo)
As many as 60000 bees can live in 3 cubic feet of space. There are about 360000 bees in... (answered by Theo)
A bee flies at 12 feet per second directly to a flowerbed from its hive. The bee stays... (answered by ikleyn,greenestamps)
There are 2429 bees in a bee colony. The number of bees increases by ten percent the... (answered by josmiceli)
A beehive has a population of 200 bees.In one week,the population increases to... (answered by htmentor)
A farmer would like to enclose a rectangular portion of his field using fences on all... (answered by josgarithmetic)
Supplying a sheep to a family costs AU$50 and a bee hive costs AU$35. If there were 24... (answered by josgarithmetic,ikleyn,greenestamps)