Step 1

For the inequalities we make auxiliary equations.

x=0 ,x+y=4, 2x+y=5

x>=0

\(\displaystyle{x}+{y}\le{4}\)

\(\displaystyle{2}{x}+{y}\le{5}\)

x=0

x+y=4

2x+y=5

Step 2

Then we make table for the equations and graph:

Step 4

Then shade the regions according to the inequalities.

For \(\displaystyle{x}\ge{0}\), shade the right side of x=0

For \(\displaystyle{x}+{y}\le{4}\), shadetowards (0,0) because x=0, y=0 satisfies the inequality.

For \(\displaystyle{2}{x}+{y}\le{5}\), shade towards (0,0) because x=0, y=0 satisfies the inequality.

So the common region is the shaded region in black.

For the inequalities we make auxiliary equations.

x=0 ,x+y=4, 2x+y=5

x>=0

\(\displaystyle{x}+{y}\le{4}\)

\(\displaystyle{2}{x}+{y}\le{5}\)

x=0

x+y=4

2x+y=5

Step 2

Then we make table for the equations and graph:

Step 4

Then shade the regions according to the inequalities.

For \(\displaystyle{x}\ge{0}\), shade the right side of x=0

For \(\displaystyle{x}+{y}\le{4}\), shadetowards (0,0) because x=0, y=0 satisfies the inequality.

For \(\displaystyle{2}{x}+{y}\le{5}\), shade towards (0,0) because x=0, y=0 satisfies the inequality.

So the common region is the shaded region in black.