Question

According to projections through the year 2030, the population y of the given state in year x is approximated by State A: - 6x + y = 11,400 State B: - 136x + y =9,000 where x = 0 corresponds to the year 2000 and y is in thousands. In what year do the two states have the same population?

Answer 1

The two states have the same population in the year 2018.

Step-by-step explanation:

To find the year when the two states have the same population, we need to solve the system of equations -6x + y = 11,400 and -136x + y = 9,000. We can do this by substituting one equation into the other.

First, we solve the first equation for y in terms of x: y = 6x + 11,400. Then we substitute this expression for y in the second equation: -136x + (6x + 11,400) = 9,000. Simplifying this equation gives us -130x = -2400. Dividing by -130, we find that x = 18.46.

Rounding to the nearest whole number, we find that the two states have the same population in the year 2018.