help with word problem of system of equations You are testing two fertilizers on bamboo plants $c$ and $d$. Plant $c$ is $5$ cm tall and growing at at a rate of $3$ cm/day. Plant $d$ is $1$ cm tall and growing at a rate of $4$ cm/day. When will the plants be the same height?
I need to write the system of equations for the problem so I need two equations, can someone please point me in the correct direction?
Thanks
 A: If you wanted to solve this in another way, you could notice that each day, plant d will gain 1 cm on plant c.  Thus, the initial height difference is the number of days until the plants will have the same height which is 4 days.
A: Let $x$ be the number of days.  You are given that the height of c is $h_c=5+3x$ and the height of d is $h_d=1+4x$  These are equal when $5+3x=1+4x$  Can you solve this?
A: Think about the problem in the following way.
You have two plants: 
Plant $c$   plant $d$ 
You know that the height of plant $c$ is already $5$cm, so that means that $5$ is a constant. You also know that height of plant $d$ is $1$cm, so you know that  $1$ is a constant. Since you have to make two linear equations, they must have this form 
$$\begin{align} 
&y = m_1x +b_1 \\
&y = m_2x +b_2 \\
\end{align}$$
You know that the $b$'s are constant in the that equation. Therefore you can insert that, into the two new equations which looks like this: 
$$\begin{align} 
&y = m_1x +5 \\
&y = m_2x +1 \\
\end{align}$$
Now, you know that plant $c$ grows at a rate of $3$cm per day. Therefore, If I want to find how many centimeters it has grown after $5$ days, I would do $3*5$. Therefore, you can say that equation for that is $3x$ where $x$ is the number of days. The same thing for plant $d$, it grows at a rate of $4$cm per day, therefore, its equation would be $4x$. So now you can fill in the portion of the equations that is left: 
$$\begin{align} 
&y = 3x +5 \\
&y = 4x +1 \\
\end{align}$$
In order to find, when they both will have the same height, you need to know when both of the equations intersect or in other words, you need to make the equations equal each other and solve for $x$. Check it out: 
$$  3x +5  = 4x +1 $$
I think, you can take it from here :) If you have any questions, comment and I will try to clarify.
