Question

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

Class X1 - Maths -Linear Inequalities Page 129

Answer 1

x + y ≤6 , x + y ≥ 4

For solving this problems follow the below steps.

step1:- consider the inequations as strict equations.
x + y =6,
x + y = 4

step2:- find the points on co-ordinate axes.
for, x + y = 6
when x=0, y = 6
when, y =0, x = 0

for, x+y=4
when, x= 0, y = 4
when,y =0, x = 4

step3:- plot the graph of,
x + y = 6,
x + y = 4.

step4:- take a point(0,0) and put it in inequations.
(0)+(0)≤6 , which is true . Hence the shaded region will be towards the origin.

(0)+ (0) ≥4, which is false.hence, the shaded region will be away from the origin.

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