If we examine the system of inequalities we notice that one has a boundary line with a positive slope and the other one has a negative slope.

Positive slope : Negative slope : y 223 x - 2 y 22 - x + 5

Knowing this, we can match the positively sloped inequality with the upward slanting boundary line and vice-versa. We also label a point that is inside the shaded area. It will come in handy!

To check which inequality symbol we should replace the equal sign with, we can use the test point

(2, 6)

and substitute it into each of the inequalities. Since it is inside the shaded area each inequality should form a true statement for this point.

y 223 x - 2

SubstituteII

$x = 2$ , $y = 6$

6223 \cdot 2 - 2

▼

Simplify RHS

Multiply

6226 - 2

SubTerm

Subtract term

6224

As

6

is greater than

4,

for this to form a true statement we have to use either

>

or

\geq .

However, since the boundary line is solid, we should use

\geq .

Let's also test the point in the second inequality.

y 22 - x + 5

SubstituteII

$x = 2$ , $y = 6$

622 - 2 + 5

AddTerms

Add terms

6223

For this to form a true statement,we have to use either

>

or

\geq .

However, since the boundary lines is dashed, we should use

> .

Finally, we have the following system of inequalities.

{y \geq 3 x - 2 y > - x + 5

Exercise