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
$y < \frac{2}{3} x$
Choose a point in the lower or upper half plane created by the line
$y = \frac{2}{3} x$
The above line is the one which goes through the origin.

Now testing (1,0) yields,

$0 < \frac{2}{3} (1)$
That is,

$0 < \frac{2}{3}$
This statement is true. So we shade the lower half of
$y = \frac{2}{3} x$

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