Two bees have found a food source. The first bee’s path to the hive follows the line . The second bee’s path follows the line . Their paths cross at the hive. Use substitution to solve the problem.
What are the coordinates of the hive?
The first bee’s path to the hive follows the line: y = 4/5 x.
The second bee’s path follows the line: y = -2x + 3.
well (4/5) x = -2 x + 3
4 x = -10 x + 15
14 x = 15
x = 15/14
then y = (4/5)(15/14) = 12/14 = 6/7
(15/14 , 6/7 )
Thank you Anonymous.
I wish both of you use distinct pen names to avoid confusion.
Yes, it would be excellent if the answerer "Anonymous" (the one who gave all those numbers) would choose a distinct screen name to identify him/herself so there's no confusion with the others who go by Anonymous.
To find the coordinates of the hive, we need to solve the system of equations formed by the two paths of the bees. The first bee's path can be represented by the line y = 2x - 3, and the second bee's path by the line y = -x + 5.
To use substitution, we can solve one equation for one variable and then substitute that expression into the other equation.
Let's solve the first equation, y = 2x - 3, for y:
y = 2x - 3
Now we can substitute this expression for y in the second equation, y = -x + 5:
2x - 3 = -x + 5
Next, we can solve this equation for x:
2x + x = 5 + 3
3x = 8
x = 8/3
Now we can substitute the value of x back into the first equation to find y:
y = 2(8/3) - 3
y = 16/3 - 3
y = 16/3 - 9/3
y = 7/3
Therefore, the coordinates of the hive are (8/3, 7/3).