Question

Question 2 Solve the following system of inequalities graphically: 3x + 2y ≤ 12, x ≥ 1, y ≥ 2

Class X1 - Maths -Linear Inequalities Page 129

Answer 1

3x + 2y ≤12 , x≥1 and y≥2

For solving this type of problems follow the below steps :

step1:- consider the inequations as strict equations .
e.g 3x + 2y = 12
x = 1
y =2

step 2:- find the point for , 3x + 2y = 12; on x-axis and y-axis .
when, x = 0, y = 6
when,y = 0, x = 4

step3:- plot the graph.
For , 3x + 2y , use the above data's
graph of x = 1, is a straight line parallel to y-axis.
graph of y = 2, is a straight line parallel to y-axis.

step4:- take a point (0,0) and put it in above all inequations.
e.g. 3(0)+2(0)≤12 , which is true.
So, shaded region will be towards the origin .
(0) ≥ 1 , which is false.
so, the shaded region will be away from the origin.
(0) ≥2 , which is false .
so, the shaded region will be away from the origin.

see graph, shaded region shows the graph of given inequations.