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 \(x > -1\).
Verified Correct Answer: .
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #54714)