Question

Draw the graph of given inequality. I x - y I = 2​

Answer 1

Answer:

ANSWER

First we solve x+2y≤10

Lets first draw graph of

x+2y=10..........(1)

Putting x=0 in (1)

0+2y=10

2y=10

y=

2

10

y=5

y=0 in (1)

x+2(0)=10

x+0=10

x=10

Drawing graph

Refer fig.1

x010

y50

Points to be plotted are (0,5),(10,0)

Checking for (0,0)

Putting

x=0,y=0

x+2y≤10

0≤10

Which is true

So, we shade left of line.

Now we solve x+y≥1

Lets first draw graph of

x+y=1..........(2)

Putting y=0 in (1)

x+0=1

x=1

Putting x=0 in (1)

0+y=1

y=1

Drawing graph

Refer fig .2

x01

y10

Points to be plotted are (0,1),(0,1)

Checking for (0,0)

Putting

x=0,y=0

x+y≥1

0+0≥1

0≥1

Which is false

Hence origin does not lie in plane x+y≥1

So, we shade right upper side of line

Now we solve x−y≤0

Lets first draw graph of

x−y=0..........(3)

Putting x=0 in (3)

0−y=0

−y=0

y=0

Putting y=2 in (2)

x−2=0

x=0+2

x=2

Drawing graph

Refer fig. 3

x02

y02

Points to be plotted are (0,0),(2,2)

Checking for (10,0)

Putting

x=10,y=0

x−y≤0

10−0≤0

10≤0

Which is false

Hence (10,0) does not lie in plane x>y

So, we shade left side of line.

Also, given

Refer fig. 4

x≥0,y≥0

So shaded region will lie in first quadrant.

Hence the shaded region represents the given inequality.