Which system of inequalities is represented on this graph?

Question

asked Dec 7, 2020 75.6k views

2 Answers

Fabio Rosati · Answer 1 · 2020-12-11T02:39:23+0000

Answer:

The correct option is 2.

Explanation:

If a line passes through two points
(x_1,y_1) and
(x_2,y_2) , then the equation of line is

y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)

From the given graph it is clear that the solid line passes through the points (0,2) and (1,0). So, the related equation of solid line is

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

y-2=-2x

Add 2 on both sides.

y=-2x+2

The sign of inequality must be ≤ because the points on the line are included in the solution set and the shaded region is below the line.

$y\leq -2x+2$ .... (1)

From the given graph it is clear that the solid line passes through the points (0,-1) and (1,0). So, the related equation of solid line is

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

y+1=x

Subtract 1 from both sides.

y=x-1

The sign of inequality must be < because the points on the line are not included in the solution set and the shaded region is below the line.

y<x-1 .... (2)

The system of inequalities is

$y\leq -2x+2$

y<x-1

Therefore, the correct option is 2.