Question

A lemon tree is 1 feet tall and grows at a constant rate of 2 feet each year, An apple tree is 2 feet tall and grows at a constant rate of 1 foot each year, Write and solve a system of linear equations to model this problem,Type in the ordered pair that is the solution to your linear equation.

Answer 1

To model the problem, we set up a system of linear equations. The solution to the system is (1, 3), meaning the lemon tree is 1 foot tall and the apple tree is 3 feet tall after 1 year.

Step-by-step explanation:

To model the problem, we can set up the following system of linear equations:

Let L represent the height of the lemon tree (in feet) and let A represent the height of the apple tree (in feet).

For the lemon tree, we have the equation L = 1 + 2t, where t represents the number of years.

For the apple tree, we have the equation A = 2 + t.

To find the solution to the system of equations, we can solve them simultaneously.

Substituting the second equation into the first equation, we get (2 + t) = 1 + 2t.

Simplifying the equation, we get t = 1.

Substituting t = 1 into the second equation, we get A = 2 + 1 = 3.

Therefore, the solution to the system of linear equations is (1, 3), which means that the lemon tree is 1 foot tall and the apple tree is 3 feet tall after 1 year.