Question

Question 5 Solve the following system of inequalities graphically: 2x – y > 1, x – 2y < –1

Class X1 - Maths -Linear Inequalities Page 129

Answer 1

2x - y >1 , x - 2y <-1

For the solving of this type of problems follow the below steps.

step1:- consider the inequations as strict equations.
2x - y = 1
x - 2y = -1

step2:- find the points on co-ordinate axes.
for , 2x - y = 1
when, x = 0, y = 1
when, y = 0, x = 1/2

for, x - 2y =-1
when, x = 0,y = 1/2
when, y=0, x =-1

step3:- plot the graph of ,
2x - y =1
x - 2y =-1

step4:- take a point (0,0) and put it in inequations.
2(0)-(0)>1, which is false. Hence, the shaded region will be away from the origin.

(0) - 2(0)<-1,which is false.hence, shaded region will be away from the origin.

see attachment, common shaded region shows the solution of the inequalities.