Answer:
To find the year when State B overtook State A in population, we need to solve the given equations simultaneously and find the values of x and y that satisfy both equations.
State B: 8y - 3x = 137
State A: 14y - x = 295
We can use the method of substitution to solve this system of equations. Rearranging the equations, we have:
State B: 3x = 8y - 137 (equation 1)
State A: x = 14y - 295 (equation 2)
Substitute equation 2 into equation 1:
3(14y - 295) = 8y - 137
Simplify and solve for y:
42y - 885 = 8y - 137
42y - 8y = 885 - 137
34y = 748
y = 748/34
y ≈ 22
Now, substitute the value of y back into equation 2 to find the corresponding x value:
x = 14(22) - 295
x = 308 - 295
x = 13
Therefore, State B overtook State A in population approximately 13 years after the year 2000, which corresponds to the year 2013.
To find the population at that time, we substitute the values of x and y into either equation. Let's use equation 2:
x = 14y - 295
x = 14(22) - 295
x = 308 - 295
x = 13
The population at that time (year 2013) was approximately 13 million.
Therefore, the year when State B overtook State A in population was 2013, and the population at that time was approximately 13 million.
Step-by-step explanation:
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