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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 )
• 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?
• All integers can be written as a fraction with a denominator of 1. Since that concept is taught when students learn fractions, it is expected that you have remembered that information for lessons that come later (like this one).

So, any slope that is a number like 5 or -3 should be written in fraction form as 5/1 or -3/1.

Hope this helps.
• 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.
• 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
• 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.
• 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.