Describe a system of linear inequalities for which there is no solution.?

Answer 1

4 questions in a row? Answer: DO YOUR OWN WORK!!!!

And wake up during class once in a while...

Answer 2

Do you mean like an example? How about:

y > x + 1
y < x

This system of linear inequalities has no solution. To prove it has no solution, let's assume there does exist solutions and obtain a contradiction.

let (x1, y1) be the solution. Then

y1 > (x1 + 1)
y1 < x1

If we add 1 to both sides of the second inequality, we obtain

(y1 + 1) < (x1 + 1), which is another way of saying

(x1 + 1) > (y1 + 1). We also have y1 > x + 1; therefore

y1 > (x1 + 1) > (y1 + 1)

Which means that

y1 > (y1 + 1), and, subtracting y1 both sides,
0 > 1. This is a contradiction.

So we conclude there is no solution.

Answer 3

That would be a pair of parallel lines, the solutions to which are on opposite sides of the lines. For example,
y < 2x + 3
y > 2x + 5

Another way this could happen is if the inequalities are not in the same plane. (skew lines)

Answer 4

Start with a set of parallel lines and then add the inequalities in the right direction. Here is one example.

x + y - 1 ≤ 0
x + y - 2 ≥ 0

Answer 5

y = 2x + 3
y = 2x + 4

as long as the coefficent in front of the x is the same in both equation the answer will always be no solution, unless the both equations are the same then the answer would be infite solutions.

Answer 6

some tricks: $5/day for different pets. what share different pets? y So it may fee $5*y to feed different pets for an afternoon. human beings are paying YOU, so their fee is how lots you EARN. to come again up with the gadget, ask your self what relationships you could set up given the information provided. as an occasion, you shelter at maximum 10 pets in line with day. what share pets are there? do no longer forget that each and each equation restricts the different. Please provide me terrific answer if this helped you.

Answer 7

two collinear equations with no points in common.