Mathematics

Problem

Let

x

and

y

be real numbers satisfying the simultaneous inequalities

2x-3<5y \quad\text{and}\quad y+4<3x.

Answer the following questions. a. (i) Prove that

x>1

must hold for every pair

(x,y)

that satisfies both inequalities. b. (ii) Eliminate

x

to obtain a single inequality involving only

y

that is implied by the two given inequalities. c. (iii) Hence determine the complete range of real values that

y

can take so that both original inequalities are simultaneously true.