Question

Use the data in the table below, representing both functions, to explain to your boss the solution to the system of equations and what that solution represents.

Answer 1

Answer:

According to the column of f(x), the number of imports increased by 1 for every month that passed by. That means that the slope of the equation is 1.

The coordinates for January are (1, 3). Since we already have y = 1x + b, we can solve for b.

3 = 1 * 1 + b

b + 1 = 3

b = 2

So, f(x) = x + 2.

According to the column of g(x), the number of exports increased by 2 for every month that passed by, which makes the slope of the equation 2.

The coordinates for January are (1, 1). Since we already have y = 2x + b, we can solve for b using the coordinates.

1 = 2 * 1 + b

b + 2 = 1

b = -1

So, g(x) = 2x - 1.

To find the solution to the system of equations, we can say that f(x) = y and g(x) = y. That means the two equations are y = x + 2 and y = 2x - 1. We can set the two equations equal to each other and get...

2x - 1 = x + 2

2x - x = 2 + 1

x = 3

2 * 3 - 1 = 6 - 1 = 5

3 + 2 = 5

y = 5

So, the solution is (3, 5). That means that the number of imports will be equal to the number of exports in March (3). The number of imports and exports will both be 5.

Hope this helps!