Question

According to projections through the year 2030, the population y of the given state in year x is approximated byState A: - 5x + y = 11,700State B: - 144x + y = 9,000where x = 0 corresponds to the year 2000 and y is in thousands. In what year do the two states have the same population?The two states will have the same population in the year

Answer 1

The x variable represents the year in question. The year 2000 is represented by x = 0, 2001 would be repreented by x = 1, and so on.

The year in which both states would have the same population can be determined by the value of x which satisfies both equations.

We would now solve these system of equations as follows;

`\begin{gathered} -5x+y=11700---(1) \\ -144x+y=9000---(2) \\ \text{Subtract equation (2) from equation (1);} \\ -5x-\lbrack-144x\rbrack=11700-9000 \\ -5x+144x=2700 \\ 139x=2700 \\ \text{Divide both sides by 139} \\ x=19.4244 \\ x\approx19\text{ (rounded to the nearest whole number)} \end{gathered}`

Note that x = 19 represents the year 2019

ANSWER:

The two states will have the same population in the year 2019