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.

Question

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

Answer 1

To eliminate the \(2t\) term from one of the sides of the equation while keeping the equation balanced, you should subtract \(2t\) from both sides.

Starting with the heights of the two plants:

1. \(4 + 2t = 8 + 2t\)

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

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

This simplifies to:

\[ 4 = 8 \]

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