Illustrate the following on graph paper and shade the region which satisfies all the three inequalities at the same time :
(- x + 5y leq 10 ; 3x – 4y leq 8) and (x > -1).
Explanation
Draw the table of value such that (-x + 5y leq 10 implies -x + 5y = 10)
(implies 5y = 10 + x )
(y = 2 + frac{x}{5})
and (3x – 4y leq 8 implies 3x – 4y = 8)
(y = -2 + frac{3x}{4})
Table of value for (-x + 5y = 10)
| x | -4 | 0 | 4 |
| y | 1.2 | 2 | 2.8 |
Table of value for (3x – 4y = 8)
| x | -4 | 0 | 4 |
| y | -5 | -2 | 1 |