How do you graph the system of linear inequalities 2x+1>=y and x<5 and y<x+2?

1 Answer
Jun 25, 2017

Draw solid or dashed lines corresponding to equations, then test the origin, (0,0), to shade. Where all three overlap is the final answer.

Explanation:

One way to graph a system of linear equations like this is to actually start by drawing them as if they were equalities first.

The inequality 2x+1 >= y becomes y=2x+1 When you graph that, you get
![Desmos.com and MS Paint](useruploads.socratic.orguseruploads.socratic.org)

Testing the point (0,0), you see that it's true that 1 >= 0, so shade that side. Because the inequality is "less then or equal to", you draw a solid (not dashed) line.
![Desmos.com and MS Paint](useruploads.socratic.orguseruploads.socratic.org)

Again, assume x < 5 is really just x=5. This gives:
![Desmos.com and MS Paint](useruploads.socratic.orguseruploads.socratic.org)

This time, the graph is dashed because you were given x < 5. Testing the point (0,0), it is true that x=0 is less than 5, so we shade to the left.

Finally, pretending to graph y < x+2 gives the line. We must used a dashed line and shade wherever the inequality is true. At the point, (0,0), the inequality is false, which means we must shade the other side.
![Desmos.com and MS Paint](useruploads.socratic.orguseruploads.socratic.org)

Finally, if we are to find out where ALL THREE inequality are true, you simply look for the solution where ALL THREE shaded parts overlap. That occurs here:
![Desmos.com and MS Paint](useruploads.socratic.orguseruploads.socratic.org)