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# Graphing systems of inequalities

Sal graphs the solution set of the system "y≥2x+1 and y<2x-5 and x>1.". Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Do you have an easier way to know which side to shade ?
• My method is to pick a point which will definitely lie on one side or the other (not on the line) and determine if it fits the equation. You can pick a point which is really easy; usually the origin is a good one.

7y < (3/2)x + 5
It seems annoying. Sub in the origin (0,0) and we get:
0 < 0 + 5, or 0 < 5.
That is, the xs and ys just disappear! Easy sauce! This is true, (0 is less than 5), so the side with the origin should be shaded.

Just remember to be careful with sign. For example:
7y < (3/2)x - 5
becomes:
0 < -5
Obviously false - don't shade this side. But it is easy on a quick glance to forget that 0 is actually more than -5. Sounds silly, but it's one of those silly mistakes I make - a LOT.

Hope this helps!
• im confused on how you new which way the coordinate of x>1, at about 3:2
• x=1 would be graphed as a vertical line that is on crosses the x axis at 1. Skip the rest of this paragraph if that already clicks for you. If not, you could also think of it as taking any y, the x coordinate =1, so pick any two y such as 2 and 3. Since you know x always equal 1, then you get the two points (1,2) and (1,3). If you graph the line through these two points, You will see that you get the vertical line going through the point (1,0).

So now since the inequality is > and not greater than or equal to, you use a dashed vertical line.

And not for what you asked. To figure out which side to shade, when x > 1, you can choose any point where x is greater than 1 such as (3,3) or (2,-1) and graph that point. Since that is a point you want to include, and you see that point is on the right, you would shade the area on the right. After a couple times it will just click that x > any number is a dashed vertical line at that the point (0,that number) shaded on the right.

I hope that helps.
• Why is my graphing calculator making X>1 different than the way your doing? It's making a line on Y 1. Please help if this makes any sense to anyone who reads this.
• I believe that you have to type it in a different way.
• How do you tell which side of the line that you shade?
• For Example:
y is equal to or GREATER than 2x+1
since y is greater than the line itself or the points on the line, you would shade up.

x is equal to or LESS than 1
since we are talking about s values, we should shade right or left not up or down. Also since x is LESS than one we should shade everything to the left of one because everything to the left of one is less than 1.

Hope that helps :)
• Is there a way to solve a system of inequalities without graphing?
• What if y has a number next to it like for example 3y, but has the other variable without a number...like 3y < -x-1 ....what you do then
• Just divide both sides by 3 to get rid of the y's coefficient. :) So...3y < -x-1 would be y < (-x-1)/3
• So we just memorize what goes on top and bottom? Any tips/ tricks?
• 1015809,

Yes. Memorize these facts:

If the inequality is < or > (with no equal to), the line is dashed.

If the inequality is <= or >= (contains equal to), the line is solid.

If the inequality is < or <=, shade below the line.

If the inequality is > or >=, shade above the line.
• how do you know if you shade above or below?
• Try one "test" point and see if it works. If it does, you shade the side that point is on. If it doesn't, you shade the other side. For example, if you have y>5, then if your test point is y =6, you find 6>5, which is true, so you shade that side. If you chose y = 4 for your test point, then you have 4 >5, which is not true, so you shade the other side.
• I still don't understand which part of the graph to shade..heellpp!