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You buy a tree That is 7" high and plant it in your front yard and it grows 5 inches every year! You plant an Oak that is 11" high and grows 3 inches per year!
1. Write two equations to show the height of each tree at any given time (one equation for each tree). Define the variables that you use. Make sure you specify the units.
2. Solve the system to find out how long it takes for the trees reach the same height.
3. Interpret your answer in a complete sentence.

Sagot :

Problem 1

x = number of years

y = height of the tree in inches

The equation for the first tree (your teacher doesn't mention the type of it) is y = 5x+7.

The 5 represents the slope or rate of change. It tells us how fast the tree is growing per year. The 7 at the end is the y intercept, and the starting amount. Refer to y = mx+b form.

Similarly, the equation for the second tree (oak tree) is y = 3x+11 because it starts off at a y intercept of 11 inches and increases by 3 inches per year, aka the slope.

I recommend making a table of values to see how each tree grows throughout the years.

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Answer:

The two equations are

y = 5x+7

y = 3x+11

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Problem 2

Let's use substitution to solve for x and y

y = 3x+11

5x+7 = 3x+11 .... replace y with 5x+7

5x-3x = 11-7

2x = 4

x = 4/2

x = 2

Use this x value to find y

y = 3x+11

y = 3*2+11

y = 6+11

y = 17

Or you could say

y = 5x+7

y = 5*2+7

y = 10+7

y = 17

We get the same y value either way, which helps confirm the answer.

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Answer:

(x, y) = (2, 17)

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Problem 3

The result of the previous problem was (x, y) = (2, 17) which is a compact way of saying that x = 2 and y = 17 pair up together.

Going back to how we defined x and y, we can see that x = 2 means that 2 years have passed and y = 17 means that both trees are 17 inches tall.

Interpretation: At the 2 year mark, both trees are 17 inches tall.

Note: 17 inches = 12 in + 5 in = 1 ft + 5 in

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