How to Graph Systems of Inequalities on the TI-84 Evo

The TI-84 Evo graphs inequalities with a built-in app called Inequality Graphing, one of the icons on the grid that opens when you press on. Type each inequality and the app shades its solutions, and when you graph a whole system it can shade just the region where everything overlaps.

Open the Inequality Graphing app

  1. Press on for the app grid, and arrow onto the shaded-triangles icon. The bar along the top names whatever is highlighted, so it reads INEQUALITY GRAPHING when you have the right one. If the icon is missing from your grid, a full memory reset has removed it along with the other built-in apps, and restoring your missing apps brings it back.
    The TI-84 Evo app grid with the Inequality Graphing icon highlighted and INEQUALITY GRAPHING named in the title bar
  2. Press enter to open it. A reminder box pops up pointing at the app's inequality menu, which comes up later in this guide, so press enter again to close it. You land on a list of lines from Y1 to Y8 that works just like the editor for ordinary graphing, with a color square in front of each line.

Type the first inequality

The example system here is y ≤ x + 2 and y > −x + 4. Everything works like typing a normal function except one move: the = sign becomes an inequality symbol through a pop-up box.

  1. Press the left arrow twice to select Y1's line options. The first press puts the cursor on the = sign, and the second highlights the whole front of the line, color square and all, with [enter] TO MODIFY in the status bar. Press enter and the settings box pops up.
  2. Pick ≤ on the middle row. Arrow down to the row showing the = sign, then arrow right until it shows ≤. The STYLE row underneath previews which side of the line will shade.
    The Inequality Graphing settings box on the TI-84 Evo with the relation row set to less than or equal
  3. Select OK, then type the right side. Arrow down to OK and press enter, then arrow right back onto the line and type X + 2, using the X key just to the right of alpha.
    The TI-84 Evo Inequality Graphing editor with Y1 set to less than or equal X plus 2
  4. Press graph. The boundary line draws solid, because ≤ keeps the points on the line, and the whole region below it fills in blue. Every shaded point is a solution of y ≤ x + 2.
    The TI-84 Evo graphing y less than or equal to x plus 2 with a solid line and the region below shaded

Make it a system

  1. Press y= to come back to the editor. Then set up the second line the same way: arrow down to Y2, press the left arrow twice to select its options, and press enter.
  2. Pick > this time, select OK, and type −X + 4. Use the (-) negative key on the bottom row for the sign in front of X.
    The TI-84 Evo Inequality Graphing editor with Y1 less than or equal X plus 2 and Y2 greater than negative X plus 4
  3. Press graph. The new boundary comes out dashed, because > is strict and points on the line itself don't count, and the red shading sits above it. The system's solutions are the region where the two shadings overlap.
    The TI-84 Evo graphing the system y less than or equal x plus 2 and y greater than negative x plus 4, with both shadings overlapping

Shade just the solution region

On a crowded window the overlap can be hard to pick out, so the app has a view that shades only the solution region. It lives in the menu the opening reminder pointed at.

  1. Press 2nd, then trace. The blue calc label above trace is the menu the app calls [2nd][calc]. It opens on a CALCULATE tab, so arrow right to the INEQUALITY tab.
    The INEQUALITY tab of the TI-84 Evo calc menu with Boundary Intersections, Inequal Intersection and Union
  2. Scroll down to 2:Inequal Intersection and press enter. The graph redraws with only the overlap shaded. Every point in that region satisfies both inequalities at once.
    The TI-84 Evo shading only the solution region of the system after choosing Inequal Intersection
  3. Mark the corner with 1:Boundary Intersections. Open the same menu again (2nd, then trace, then arrow right) and press enter on the first item. The point where the boundary lines cross gets a marker, and its coordinates print along the bottom of the screen: X=1 and Y=3.
    The TI-84 Evo marking the corner of the solution region at X equals 1, Y equals 3 with Boundary Intersections

Vertical inequalities like x < 3

The regular graphing editor can't draw x < 3, because there is no y in it. This app can. Inside the editor, press y= and the list flips from Y lines to X lines. Set X1's symbol to < through the same pop-up box, then type 3:

The X= side of the TI-84 Evo Inequality Graphing editor with X1 set to less than 3

Press graph and you get a dashed vertical line at x = 3 with everything to its left shaded. Press y= again to flip back to the Y side.

The TI-84 Evo graphing x less than 3 as a dashed vertical line with the region to its left shaded

Good to know

  • The special views stick. Inequal Intersection and Union stay on for every new graph until you quit the app and open it again. To quit, arrow up past Y1 to the row of tabs, arrow across to OPTIONS, press enter, and choose Quit App. Your inequalities are still in the editor when you come back.
  • Union is the other combined view. Choosing 3:Union in the same menu shades every point that satisfies at least one of the inequalities instead of all of them.