How is graphing a sysyem of linear inequalities the same as graphing a system of linear equations? Different?

Question

How is graphing a sysyem of linear inequalities the same as graphing a system of linear equations? How is it different??

Answer 1

When you graph a set of linear equations, the solutions all lie on the line itself. Therefore the solution of the set of equations is the single point where all lines cross each other.

When you graph a set of inequalities, the solutions all lie either above (>) or below (<) the line (or on the line for <= and >=). That's why you shade areas. Then the solution of the set of inequalities is the region where all the shaded areas for all the equations overlap.

Answer 2

Think about how you've done inequalites on the number line. For instance, they'd ask you to graph something like x > 2. How did you do it? You would draw your number line, find the "equals" part (in this case, x = 2), mark this point with the appropriate notation (an open dot or a parenthesis, indicating that the point x = 2 wasn't included in the solution), and then you'd shade everything to the right, because "greater than" meant "everything off to the right". The steps for linear inequalities are very much the same.

Answer 3

inequalities express a domain such as all y < x-5 whereas a linear equation defines only a set of points and a system of linear equations can define either a single point of intersection or set of points on each line.

Answer 4

both show the common answer(s).However, the system of linear inequalities shows multiple(or infinite) solutions whereas a sysem of linear equations shows only 1 solution.

Answer 5

You draw lines just as you would with equations.
Then, unline equations, you shade area above or below the line.

Answer 6

read through your textbook.. is hard to sketch the graph here..