Which of the following conclusions must be true?

Question

y<x+k₁

y>2x+k₂

 

Suppose that on a coordinate plane, (0,0) is a solution to the system of inequalities given above. Which of the following conclusions about k₁ and k₂ must be true?

 

A. k₁<k₂

B. k₂<k₁

C. |k₁|<|k₂|

D. k₁=-k₂

Answer 1

y < x + k₁

y > 2x + k₂

2x + k₂ < y < x + k₁       write as single inequality

2x + k₂ < x + k₁                 

x + k₂ < k₁                            subtract x from all arguments

 

What do you conclude about k₁ and k₂?