29 Solve the following system of inequalities graphically 2x+y≤24, - Maths - Linear Inequalities

Question

29 Solve the following system of inequalities graphically
2x+y ≤ 24, x+y < 11, 2x+5y ≤ 40, x,y ≥ 0

Neha Sethi · Accepted Answer

Dear student
Converting the inequations  into equations we get,2x+y=24;x+y=11;2x+5y=40;x=0;y=0
Now,
2x+y=24

x
y

0
24

12
0

x+y=11

x
y

0
11

11
0

2x+5y=40

x
y

0
8

20
0

Since (0,0) satisfy the inequation 2x+y≤24
So, the portion contaning the originrepresents the solution set of the inequation 2x+y≤24
Since (0,0) satisfy the inequation x+y<11
So, the portion contaning the originrepresents the solution set of the inequation x+y<11
Since (0,0) satisfy the inequation 2x+5y≤40
So, the portion contaning the originrepresents the solution set of the inequation 2x+5y≤40
So the common region of the above 5 regions represents the solution set of the given linear constraints as shown in the figure below
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5a9f9d0917bb7%20png"
style="width: 1022px; height: 361px;">
Regards

29. Solve the following system of inequalities graphically 2x+y ≤ 24, x+y < 11, 2x+5y ≤ 40, x,y ≥ 0

29. Solve the following system of inequalities graphically
2x+y $\leq$ 24, x+y < 11, 2x+5y $\leq$ 40, x,y $\geq$ 0