Question

Please Help!!

Which graph represents the solution set of the system of inequalities?

{y<2/3x
{y≥−x+2

Answer 1

When you see questions of this nature, test the individual inequalities and look out for their intersection.

For

`y < (2)/(3) x`
Choose a point in the lower or upper half plane created by the line

`y = (2)/(3) x`
The above line is the one which goes through the origin.

Now testing (1,0) yields,


`0 < (2)/(3) (1)`
That is,


`0 < (2)/(3)`
This statement is true. So we shade the lower half of

`y = (2)/(3) x`

For

`y \geqslant - x + 2`
We test for the origin because, it is not passing through the origin.


`0 \geqslant - (0) + 2`
This yields

`0 \geqslant 2`
This statement is false so we shade the upper half.

The intersection is the region shaded in B. The top right graph