# How do you graph the system y>= x+2 and y> 2x+3?

Jul 1, 2015

y≥x+2 and $y > 2 x + 3$ is true when you are inside the darker area except on the dotted line.

#### Explanation:

To respect conditions, you need to respect each of them.

Step 1 : Make a graph of all the points who is respecting y≥x+2

All the blue area regards the first condition.
Example : The point A(0,4) respects y≥x+2 because 4 ≥ 0+2

Step 2 : Do the same thing on the same graph with $y > 2 x + 3$
Be careful we have a ">" and not "≥" i.e : If a point is on the linear equation : "y = 2x+3" (the dotted line) it won't respect the 2nd condition.

Then we have this result :

A(0;4) is in the darker area <=> A respect y≥x+2 and $y > 2 x + 3$

$\to \textcolor{g r e e n}{4 \ge 0 + 2}$
$\to \textcolor{g r e e n}{4 \ge 2 \cdot 0 + 3}$

Note : Sorry for my English ;)