Question

What system of linear inequalities is shown in the graph?

Enter your answers in the boxes.

Answer 1

`y > 2x - 3`

`y \geqslant - (1)/(2)x + 2`

Answer 2

`2y+x\geq4`

`2x-y>3`

Explanation:

Equation of a line passes through (a,b) and (c,d) :-

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

Equation of solid line passes through (4,0) and (0,2) :-

`(y-0)=(2-0)/(0-4)(x-4)\\\\ y=(-1)/(2)(x-4)\\\\ 2y=-x+4\\\\ 2y+x=4`

Since graph is shaded above the line, so the inequality represents solid (line is included) line:

`2y+x\geq4`

Equation of dashed line passes through (0,-3) and (1,-1) :-

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

Since graph is shaded above the line, so the inequality represents dashed ( line is not included ) line:

`2x-y>3`

Hence, the system of linear inequalities is shown in the graph :-

`2y+x\geq4`

`2x-y>3`