In attempting to solve the system of equations and , John graphed the two equations on his graphing calculator. Because he saw only one line, John wrote that the answer to the system is the empty set. Is he correct? Explain your answer.

The correct answer is NO.

Step-by-step explanation:

John is graphing two lines with equations say ax + by + c = 0 and dx + ey +f =0 on his graphing calculator.

For John to get a unique solution the coefficients should follow the following condition . So when he plots the lines he get an intersecting pair of lines.

For John to get no solution the coefficients should follow the following condition . When we plot in this case we get two parallel lines.

For John to get an infinite many solution the coefficients should follow the following condition . And when we plot the lines in this case we get one line superimposed on the other.

Since after graphing, John sees only one line, the lines must have superimposed on one another giving John an infinite number of solutions.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

the answer is y = 11.54

hope this : )