Question

ion.A 4 cm bean plant grows at a rate ofcm per week. A5.5 cm flower grows at a rate of cm per week. If h isthe height of the plant in centimeters and t is thenumber of weeks, then the system of equations is:h = 2t+4h = t +5.5The solution to the system,plants will both bemeans that thecentimeters tall afterweeks.

Answer 1

`\begin{gathered} h=7 \\ t=6 \end{gathered}`

Step-by-step explanation

Given;

`\begin{gathered} h=(1)/(2)t+4..........1 \\ h=(1)/(4)t+5.5.............2 \end{gathered}`

Substitute the value of h in equation 1 and 2;

`\begin{gathered} (1)/(2)t+4=(1)/(4)t+5.5 \\ \end{gathered}`

Subtract 4 from both sides;

`\begin{gathered} (1)/(2)t+4-4=(1)/(4)t+5.5-4 \\ (1)/(2)t=(1)/(4)t+1.5 \\ (1)/(2)t=0.25t+1.5 \\ \end{gathered}`

Subtract 0.25t from both sides;

`\begin{gathered} (1)/(2)t-0.25t=0.25t+1.5-0.25t \\ 0.25t=1.5 \\ t=(1.5)/(0.25) \\ =6 \\ t=6 \end{gathered}`

Substitute the value of t in equation 1;

`\begin{gathered} h=(1)/(2)t+4 \\ =(1)/(2)(6)+4 \\ =3+4 \\ =7 \end{gathered}`

Therefore, the solution of the system is h=7 and t=6 means that the given plant will both be 7cm tall after 6weeks.