Which system of linear inequalities is represented by the graph

Question

asked Jul 12, 2020 104k views

2 Answers

Mea · Answer 1 · 2020-07-16T07:41:51+0000

Answer:

The correct option is 3.

Explanation:

If a line passing through two points, then the equation of line is

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

Rel line passing through the points (0,-2) and (2,0), then related equation of red line is

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

y+2=x

y=x-2

Since the shaded region is above the line and the related line is a solid line therefore the sign of inequality must be ≥. The first inequality is

$y\geq x-2$

Blue line passing through the points (0,2) and (4,0), then related equation of red line is

y-(2)=(0-(2))/(4-0)(x-0)

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

Multiply 2 on both the sides.

2y-4=x

x+2y=4

(0,0) is in the shaded region. So, the inequity must be satisfy by (0,0).

0+2(0)=4

0=4

The related line is dotted, so the required sign of inequality is <. The second inequality is

x+2y<4

The system of linear inequalities is defined as

$y\geq x-2$

x+2y<4

Therefore the correct option is 3.