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

1 Answer
Jul 1, 2015

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#y≥x+2# and #y>2x+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#

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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>2x+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 :

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

# -> color(green)(4>=0+2)#
# -> color(green)(4>=2*0+3)#

Note : Sorry for my English ;)