Question

Which system of linear inequalities is represented by the graph

Answer 1

The Answer Too Your Question Is C

Answer 2

Answer:

The correct option is 3.

Step-by-step explanation:

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

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

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

$y-(-2)=\frac{0-(-2)}{2-0}(x-0)$

$y+2=x$

$y=x-2$

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

$y-(2)=\frac{0-(2)}{4-0}(x-0)$

$y-2=\frac{1}{2}x$

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

$x+2y$

The system of linear inequalities is defined as

$y\geq x-2$

$x+2y$

Therefore the correct option is 3.