Question

Question 3 Solve the following system of inequalities graphically: 2x + y≥ 6, 3x + 4y ≤ 12

Class X1 - Maths -Linear Inequalities Page 129

Answer 1

2x + y ≥ 6 ,3x + 4y ≤12


For solving this type of problems follow the below steps :

step1:- consider the inequations as strict equations .
e.g 2x + y = 6
3x + 4y = 12

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

step3:- plot the graph.
For , 2x + y=6 , use the above Data's
For, 3x+4y=12 ,use the above Data's.

step4:- take a point (0,0) and put it in above all inequations.
e.g. 2(0)+(0)≥6 , which is false.
So, shaded region will be away from the origin .
3(0)+4(0)≤12 , which is true.
So, the shaded region will be towards the origin.

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