Find the linear inequations for which the shaded area in Fig. 15.41 is the solution set. Draw the diagram of the solution set of the linear inequations.

In this question, we will apply the concept of a common solution area to find the signs of inequality by using their given equations and the given common solution area(shaded part).

If a line is in the form ax+by = c and c is positive constant(in case of negative c the rule becomes opposite), so there will be two cases to discuss, which are,

If a line is above origin :–

(i). If the shaded area is below the line then ax+by<c

(ii). If the shaded area is above the line then ax+by>c

If a line is below origin then the rule becomes opposite.

According to the rules the answer will be,