You plant a spruce tree that grows 4 inches per year and a hemlock tree that grows 6 inches per year. The initial heights are shown.

Question

A.Write a system of linear equations that represents the stituation.

B.Solve the system by any method. Interpret your solution.

Answer 1

Hello, Ashyln,

I don't see the initial heights, nor do I understand what solution is sought.

Equations that would describe the heights of the trees as a function of years, x, would be:

Spruce: S = 4x + I_s

Hemlock: H = 6x + I_h

where I_s and I_h are the initial heights of the Spruce and Hemlock, respectively.

I'm just guessing, but if the question is "How many years will it take before the Hemlock to reach the same height as the Spruce, we could solve for that problem.

We'll need to assume initial heights for both. I'll set the Spruce to 60 inches and the Hemlock to 10 inches:

Spruce: S = 4x + 60

Hemlock: H = 6x + 10

If we want to find the years, x, that it will take for the Hemlock to catch up to the Spruce, we set the equations equal to each other (their heights are the same).

S = H

4x + 60 = :6x + 10

-2x = -50

x = 25 years

Both trees are 160 inches tall in 25 years.

I hope this helps,

Bob

Answer 2

Most likely asking when (in years) they will be same height.

S for spruce, H for hemlock, y for year

S = 4y + initial height of S

H = 6y + initial height of H

So, set equal and solve for y.