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# Intro to graphing systems of inequalities

Learn how to graph systems of two-variable linear inequalities, like "y>x-8 and y<5-x.". Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• How do you know if the line will be solid or dotted? Does it matter?
• It does matter.

It will be solid if the inequality is less than OR EQUAL TO (≤) or greater than OR EQUAL TO ≥.

It will be dotted if the inequality is less then (<) or greater then (>).

Think of a simple inequality like x > 5.
x can be ANY value greater then 5, but not exactly 5. x could be 5.000000000001, but not 5. They put the dotted line because its saying 'this is where the inequality will work, except right on this line'.
• Can systems of inequalities be solved with subsitution or elimination? or only by graphing? thanks! :)
• the best method is cross multiplication method or the soluton using cramer rule...... it might seem lengthy but with practice it is the easiest of all and always reliable..
• If the slope was 2 would the line go 2 up and 2 across, 2 up and 1 across, or 1 up and 2 across?? Thanks!
• If the slope was 2 it would go up two and across once.
Slope = y / x
2 = 2/1
2 = y ( Vertical )
1 = x ( Horizontal )
• how do you graph an inequality if the inequality equation has both "x" and "y" variables?
• It depends on what sort of equation you have, but you can pretty much never go wrong just plugging in for values of x and solving for y.
• Why is the slope not a fraction ? How do I know I have to only go over 1 on the x axis if there isn't a number to specify that I have to?
• Hey AydanV. I am also a homeschooler, so firstly, it is a pleasure to find someone who also pursuing knowledge on his own. The slope is not a fraction in this particular case because it is a 45º line, which means, if it rises 1 unit, it will go left also one unit. I did not get the second part of your question, but if you reword it i am sure I can help you further.
• wait if you were to mark the intersection point,would the intersection point be inclusive of exclusive if one of the lines was dotted and the other was not
• The intersection point would be exclusive. The easiest way to see this is with an example:
If we had the two lines x >= 3 and y < 6, the intersection point (3,6) wouldn't be a solution, because to be a solution, it would have to fulfill both equations:
3 >= 3
6 !< 6
Since 6 is not less than 6, the intersection point isn't a solution.
• how do you know its a dotted line?
• Hint: to get ≥ hold down ALT button and put in 242 on number pad, ≤ is ALT 243. Makes it easier than words
• Without Graphing, would you be able to solve a system like this:
Y+x^2-2x+1
Y=x+1
• Yes! I think you meant to write y = x^2 - 2x + 1 instead of y + x^2 - 2x + 1. So, if: y = x^2 - 2x + 1, and
y = x + 1, using substitution we get, x + 1 = x^2 - 2x + 1, subtracting 1 from each side we get,
x = x^2 - 2x, adding 2x to each side we get 3x = x^2, dividing each side by x we get, 3 = x, so y = 4. So, yes, you can solve this without graphing.