Answer:
[tex]3y-x<6[/tex]
[tex]2x+y\leq2[/tex]
Step-by-step explanation:
Equation of line that passes two points (a,b) and (c,d) :
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Dotted line passes through (0,2) and (-3,1).
Equation of Dotted line :
[tex](y-2)=\dfrac{1-2}{-3-0}(x-0)[/tex]
[tex](y-2)=\dfrac{-1}{-3}x[/tex]
[tex]3(y-2)=x[/tex]
[tex]3y-6=x[/tex]
[tex]3y-x=6[/tex]
Inequality for dotted line (values on line is not included for dotted)
[tex]3y-x<6[/tex] (shaded below )
Solid line passes through (0,2) and (1,0)
[tex](y-2)=\dfrac{0-2}{1-0}(x-0)[/tex]
[tex]y-2=-2x[/tex]
[tex]2x+y=2[/tex]
Inequality for dotted line (values on line is included for solid line)
[tex]2x+y\leq2[/tex] (shaded leftwards )
∴ System of linear inequalities is shown on the graph:
[tex]3y-x<6[/tex]
[tex]2x+y\leq2[/tex]
