Question

Please help me to write a system of linear equations that represents the situation. Will your friend’s hair ever be as long as her cousin’s hair? If so, in what month?

Answer 1

Given the information in the table, we can calculate the slope of the line using the equation:

`m=(y_2-y_1)/(x_2-x_1)`

Where x₁ and x₂ are the months number 3 and 8, respectively. y₁ and y₂ are the lengths of the hair in those months. Then:

`\begin{gathered} \text{Friend}\colon m_F=(6.5-4)/(8-3)=(2.5)/(5)=0.5 \\ \text{Cou}\sin \colon m_C=(9-7)/(8-3)=(2)/(5)=0.4 \end{gathered}`

Now, using the point-slope form of the equation of the line:

`\begin{gathered} \text{Friend}\colon y-4=m_F(x-3)\Rightarrow y=0.5x+2.5_{} \\ \text{Cousin}\colon y-7=m_C(x-3)\Rightarrow y=0.4x+5.8 \end{gathered}`

To calculate if their hair length would ever be equal, we use the equations above:

`\begin{gathered} 0.5x+2.5=0.4x+5.8 \\ 0.1x=3.3 \\ x=33 \end{gathered}`

They will be equal after 33 months.