Question

Can u please graph the intersection of the coordinate plane?

Answer 1

Given:

`x-y\le3`
`x>-5`

Consider the equation of the first inquality.

`x-y=3`

`y=x-3`

Set x=0, we get

`y=0-3=-3`

We get the point (0,-3).

Set x=3, we get

`y=3-3=0`

We get the point (3,0).

Mark the points (0,-3) and (3,0) and draw a ray to join the points.

Let a point (0,0) from the left of the line that does not lie on the line.

substitute x=0, y=0 in the given inequality, we get

`0-0\le3`
`0\le3`

This is true so the point from the left side of the equation line on the inequality.

Now shade the left side of the line.

The next inequality is

`x>-5`

Draw a dotted vertical line that parallels the y-axis at the point (-5,0).

And the values are greater than -5, so shade the right side of the line.

The graph is

The intersection of the coordinates is the grey shaded region.

The whole region lies between (-5,0),(-5,-8), (0,-3) and (3,0).

We can see that (0,0) is also the intersection of the given inequalities.