Question

The graph below shows the solution to which system of inequalities

Answer 1

The answer is
the option A
The graph shows the solution of the system of inequalities
y> -3
y<=-x

using a graph tool
see the attached figure

Answer 2

Answer: The correct option is A.

Explanation:

From the given figure it is noticed that at y = -3 there is dotted line and the it shaded in upward direction.

Since it is a dotted line -3 will not included. It means it will take all value of y which are more than -3.

$y>-3$    ......(1)

The second line passing through the origin, slope is negative and change in y is same as change in x, therefore the equation of line is y = -x.

The line shaded downwards it means all the point in shaded region will satisfies the inequality.

The point (-5,1) is in shaded region. check this point for the line y=-x

$1=-(-5)$

$1=5$

We know that 1 is less than 5 and it is not a dotted line it means the sign of inequality is less than or equal to. so, the equation is,

$y\leq x$

Therefore, the correct option is A.