(a) 
In the diagram, BA is parallel to DE. Find the value of x.
(b) Illustrate graphically and shade the region in which inequalities \(y – 2x < 5 ; 2y + x \geq 4 ; y + 2x \leq 10\) are satisfied.
Explanation
(a) 
Draw RC produced to E parallel to DE.
\(\therefore < BCR = 52°\) (alternate angles BA//RC)
also < RCD = 48° (alternate angles RC//DE)
\(x° = 360° - (52° + 48°) = 360° - 100° = 260°\) (angles at a point = 360°)
(b) \(y - 2x < 5 ... (i)\)
\(2y + 2x \geq 4 \implies y + x \geq 2 ... (ii)\)
\(y + 2x \leq 10 ... (iii)\)
From (i), if \(y - 2x = 5\), when x = 0, y = 5, when x = 2, y = 9.
From (ii), if \(y + x = 2\). when x = 0, y = 2, when x = 3, y = -1
From (iii), if \(y + 2x = 10\), when x = 0, y = 10, when x = 2, y = 6.