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Sagot :

Given:

The graph of system of inequalities.

To find:

The system of inequalities.

Solution:

From the given graph it is clear that the shaded region is lies below the line y=10 and the boundary line y=10 is a solid line. So, the sign of inequality must be [tex]\leq[/tex].

[tex]y\leq 10[/tex].

The shaded region lies on the right side of the y-axis. So, [tex]x\geq 0[/tex].

Another boundary line passes through the point (0,1) and (1,2). So, the equation of the line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-1=\dfrac{2-1}{1-0}(x-0)[/tex]

[tex]y=1(x)+1[/tex]

[tex]y=x+1[/tex]

The boundary line [tex]y=x+1[/tex] is a dotted line and the shaded region lies above the boundary line, so the sign of inequality must be [tex]>[/tex].

[tex]y> x+1[/tex]

So, the required system of inequalities is:

[tex]y> x+1[/tex]

[tex]y\leq 10[/tex]

[tex]x\geq 0[/tex]

Therefore, the correct option is B.