System of Linear Inequalities

This is a graph of a linear inequality:

Graph with shaded region below the solid line y = x + 2
The inequality y ≤ x + 2

We can see the y = x + 2 line, and the shaded area is where y is less than or equal to x + 2

A Linear Inequality is like a Linear Equation (such as y = 2x+1) ...

... but it will have an Inequality like <, >, ≤, or ≥ instead of an =.

We can have more than one inequality, which makes it a system of inequalities.

A System of Linear Inequalities

The Inequality Grapher handles them beautifully, give it a try.

Is a Point Within the Inequalities?

We simply check that the point satisfies each inequality.

Check: y ≤ x + 2:

Try (3,1):

1 ≤ 3 + 2

1 ≤ 5

That's True! Let's check the other inequality:

Try (3,1):

1 ≥ −3/2

1 ≥ −1.5

That's also True!

Both inequalities are true, so the point is within the system of linear inequalities.