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 |
