Question

Question 8 Solve the following system of inequalities graphically: x + y ≤ 9, y > x, x ≥ 0

Class X1 - Maths -Linear Inequalities Page 129

Answer 1

x + y ≤9, y>x and x≥0

For solving this problem follow the below steps.

step1:- consider the inequations as strict equations.
x + y = 9,
y = x,
x = 0

step2:- find the points on co-ordinate axes.
for, x + y = 9
when, x = 0, y =9,
when, y = 0, x = 9

y = x , passing through origin(0,0)
x = 0 is coincidence with y-axis.


step3:- plot the graph,
x + y = 9,
y = x
x = 0

step4:- take a point(0,0)and put it in inequations.
(0)+(0) ≤ 9 , which is true. Hence, the shaded region will be towards the origin.

(0)>(0) , which is true. Hence, the shaded region will be towards the origin.

(0) ≥ 0 , which is true. Hence the shaded region will be towards the origin.

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