Question

This question has two parts. Be sure to answer both parts of the question. One inequality in a system is shown below. -12x + 3y > 9 PART A. Create another inequality so the system has no solution.PART B. Create another inequality so the system has infinite solutions.

Answer 1

The inequality is -12x + 3y > 9.

PART A:

The sytem has no solution if inequality does not share a common area. The inequality -12x + 3y > 9 consist the region to left of line -12x + 3y = 9. So for no solution the region to left of equation -12x + 3y = 9 is suitable.

Thus inequality for no solution is, -12x + 3y < 9.

PART B:

For infinite solution the region of both inequality must overlap each other, or the inequality is same with some multiplication of divison factor. So inequality for infinite many solutions is,

`\begin{gathered} (-12x+3y>9)*-1 \\ 12x-3y<-9 \end{gathered}`

Thus inequality for infinite many solution is 12x - 3y < -9.