Question 149483
Ok, the best way I think to solve this problem is to look at each plant as a line on a graph and at some point they're going to cross. That's when they'll be the same height.

Let's make "x" the number of years and we'll make an equation.

y is going to be the total number of feet the plant is after "x" number of years.

Plant 1: y= 2ft(starting out) + 3ft/year times x number of years so....
y= 2+3x ... you with me?
this can be written as y=3x+2 a common equation for a line.

Plant 2 is going to be the same way....

We start our with 4ft and add 1 ft each year... written as...

y= 1x + 4
or
y=x+4

if you want you can do it algebraically with a system of equations like this...

y= 3x+2
y= x+4

Multiply one equation by a number that will make the Xs opposite...
in this case it's -3

y= 3x+2
(y= x+4) times -3

Then add the two equations together
so...
 
    y= 3x+2
+ -3y= -3x-12
______________
  -2y= -10
 divide both sides by (-2) and wualla!!
    y= 5
When you plug y back into the original equation... you get...

 y= 3x+2
(5)= 3x+2
minus 2 on both sides
3=3x
divide by 3 on both sides
x=1 year!!!!

Or, if you would like you can just graph it and see where they intersect!!!

{{{graph(300, 200, -5, 5, -5, 5, x+4, 3x+2)}}}