Question

Which of the following systems of inequalities represents the graph?

Answer 1

Answer:

Option D.

Step-by-step explanation:

Consider the below figure attached with this question.

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

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

From the below figure it is clear that the a solid line passes through the points (-2,0) and (0,4). So, the equation of related line is

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

$y=2(x+2)$

$y=2x+4$

$-2x+y=4$

All area above the solid line is shaded. It means the sign of inequality is ≥.

$-2x+y\geq 4$

From the below figure it is clear that the a dashed line passes through the points (2,0) and (0,2). So, the equation of related line is

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

$y=-1(x-2)$

$y=-x+2$

$x+y=2$

All area below the dashed line is shaded. It means the sign of inequality is <.

$x+y$

System of inequality is

$-2x+y\geq 4$

$x+y$

Therefore, the correct option is D.