(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.