Question

Kudzu is a Japanese vine that was introduced in the US during the late 19th century, but was widely distributed after the dust bowl of 1930s when planted by the Civilian Conservation Corps as an aid to soil erosion. Since that time, kudzu has thrived and is now considered an invasive species. The number of acres (in thousands) covered by kudzu in Louisiana is given by the equation 3.38x - y = 6,211.69 while the acreage covered by kudzu in Alabama is given by the formula 12.29x - y = 23,801.17. In what year did both states have the same number of acreage covered by kudzu?

Answer 1

To find the year when both states had the same number of acreage covered by kudzu, we need to solve the system of linear equations for x and y.
For Louisiana:
3.38x - y = 6,211.69
For Alabama:
12.29x - y = 23,801.17
First, we can solve the system of equations by eliminating the variable y. To do this, we can multiply the first equation by 3.38 and the second equation by 1 to keep the coefficients of y the same:
11.72x - 3.38y = 21,174.23
12.29x - y = 23,801.17
Now, we can add the two equations to eliminate y:
(11.72x - 3.38y) + (12.29x - y) = 21,174.23 + 23,801.17
24.01x = 44,975.40
Now, we can solve for x:
x = 44,975.40 / 24.01
x ≈ 1,873.94
Now that we have the value of x, we can substitute it back into either of the original equations to solve for y. We'll use the Louisiana equation:
3.38x - y = 6,211.69
3.38(1,873.94) - y = 6,211.69
Now, solve for y:
y = 3.38(1,873.94) - 6,211.69
y ≈ 10,210.99
So, in the year 1,873.94 (approximately), both Louisiana and Alabama had the same number of acreage covered by kudzu.