Question

What system of linear inequalities is shown on the graph?

Answer 1

top is the dotted , bottom is the solid

Answer 2

`3y-x<6`

`2x+y\leq2`

Explanation:

Equation of line that passes two points (a,b) and (c,d) :

`(y-b)=(d-b)/(c-a)(x-a)`

Dotted line passes through (0,2) and (-3,1).

Equation of Dotted line :

`(y-2)=(1-2)/(-3-0)(x-0)`

`(y-2)=(-1)/(-3)x`

`3(y-2)=x`

`3y-6=x`

`3y-x=6`

Inequality for dotted line (values on line is not included for dotted)

`3y-x<6` (shaded below )

Solid line passes through (0,2) and (1,0)

`(y-2)=(0-2)/(1-0)(x-0)`

`y-2=-2x`

`2x+y=2`

Inequality for dotted line (values on line is included for solid line)

`2x+y\leq2` (shaded leftwards )

∴ System of linear inequalities is shown on the graph:

`3y-x<6`

`2x+y\leq2`