Ask a New Question
Menu

The relationship between time in months, t, and height in cm, h, can be represented by the equation h=4+2t for Plant A and h=8+2t for Plant C.

You just used the graph of this situation to see that there is no time when Plants A and C will be the same height. Now, let's use the equation below to confirm that there is no solution to this system. Let’s try to isolate the variable t. Since there are t terms on both sides of the equation, let’s eliminate the t term from one of the sides. What move can you make to eliminate the 2t on the left side, while keeping the equation balanced?
h=4+2t
h=8+2t
Height of Plant A
=
Height of Plant C
4+2t
=
8+2t

Add 2t to both sides

Subtract 2t from both sides

1 answer

To eliminate the \(2t\) on the left side while keeping the equation balanced, you can subtract \(2t\) from both sides.

Starting with the system of equations:

  1. \( h = 4 + 2t \) (Height of Plant A)
  2. \( h = 8 + 2t \) (Height of Plant C)

Set the two equations equal to each other because they both represent \(h\):

\[ 4 + 2t = 8 + 2t \]

Now, subtract \(2t\) from both sides:

\[ 4 + 2t - 2t = 8 + 2t - 2t \]

This simplifies to:

\[ 4 = 8 \]

Since \(4\) does not equal \(8\), this confirms that there is no solution to the system, meaning Plants A and C will never be the same height.