Question

Graph the system on inequalities:

y ≥ -2
y≤-|x-3|

What quadrant does the solution lie in?

Answer 1

The solution of the inequalities lies in 4th quadrant.

Explanation:

Given : Equation
`y\geq -2` and
`y\leq -|x-3|`

To find : Graph the solution for the following linear inequality system?

Solution :

We have to plot the given equation,

Equation 1 -
`y\geq -2` passes through (0,-2) straight line on x-axis.

Check the region by putting y=0

`0\geq -2`

True the region is towards origin.

Equation 2 -
`y\leq -|x-3|` passes through (3,0) and (0,-3)

Check the region by putting x=0 and y=0

`0\leq -|0-3|`

`0\leq -3`

False the region is away from origin.

Refer the attached figure blow.

The solution of the inequalities lies in 4th quadrant.