A region in the coordinate plane is described as follows: line is drawn with a solid line
MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Inequalities · Linear Inequalities
Problem
A region in the coordinate plane is described as follows: line ℓ1:x+y=4 is drawn with a solid line. The point (0,5) lies outside the shaded region. Line ℓ2:x−2y=1 is drawn with a dotted line. The point (3,0) lies inside the shaded region. The shaded region is the intersection of the two half-planes determined by ℓ1 and ℓ2.
(i) Write the inequality corresponding to ℓ1 that selects the correct half-plane.
(ii) Write the inequality corresponding to ℓ2 that selects the correct half-plane.
(iii) Combine your answers from parts (i) and (ii) to obtain the system of inequalities representing the shaded region.
(iv) Determine whether the point (4,2) belongs to this region. Show your working.