Question

Use the graph to determine and interpret the solution. A 4 cm bean plant grows at a rate of 1/2cm per week. A 5.5 cm flower grows at a rate of 1/4cm per week. If h is the height of the plant in centimeters and t is the number of weeks, then the system of equations is:
h = 1/2t + 4
h = 1/4t + 5.5
The solution to the system,___?___
, means that the plants will both be ___?___ centimeters tall after__?___weeks.

Answer 1

1/2t + 4 = 1/4t + 5.5
1/2t - 1/4t = 5.5 - 4
2/4t - 1/4t = 1.5
1/4t = 1.5
t = 1.5 x 4
t = 6

h = 1/2t + 4
h = 1/2(6) + 4
h = 3 + 4
h = 7

solution is (7,6)
means that the plants will both be 7 cm tall after 6 weeks

Answer 2

The solution of the system is h =7 and t = 6 means that the plants will both be 7 centimeters tall after 6 weeks.

Given that

A 4 cm bean plant grows at a rate of 1/2cm per week.

A 5.5 cm flower grows at a rate of 1/4cm per week.

If h is the height of the plant in centimeters and t is the number of weeks, then the system of equations is:

h = 1/2t + 4

h = 1/4t + 5.5

According to the question

The solution of the system of equation is;

h = 1/2t + 4

h = 1/4t + 5.5

Substitute the value of h from equation 1 in equation 2

$\rm h = \dfrac{1}{4}+5.5\\\\\dfrac{1}{2}t +4 = \dfrac{1}{4}t +5.5\\\\\dfrac{1}{2}t-\dfrac{1}{4}t = 5.5-4\\\\\dfrac{2t-t}{4} = 1.5\\\\\dfrac{t}{4} = 1.5\\\\t = 4\times 1.5\\\\t = 6$

Substitute the value of t in equation 1

$\rm h = \dfrac{1}{2}\times 6+4\\\\h = 3+4\\\\h = 7$

Hence, The solution of the system is h =7 and t = 6 means that the plants will both be 7 centimeters tall after 6 weeks.

To know more about the System of Equation click the link given below.

https://brainly.com/question/12895249