+ y ≤, 2x + y ≥ | Sharp EL9900 specs

EL-9900 Graphing Calculator

System of Two-Variable Inequalities

The solution region of a system of two-variable inequalities consists of all points (a, b) such that when x = a and y = b, all inequalities in the system are true. To solve two-variable inequalities, the inequalities must be manipulated to isolate the y variable and enter the other side of the inequality as a function. The calculator will only accept functions of the form y = . (where y is defined explicitly in terms of x).

Example

Solve a system of two-variable inequalities by shading the solution region. 2x + y ≥ 1

x 2 + y ≤ 1

Before There may be differences in the results of calculations and graph plotting depending on the setting. Starting Return all settings to the default value and delete all data.

Set the zoom to the decimal window:

ZOOM

(

ENTER

2nd F

) 7

Step & Key Operation

Display

Notes

1 Rewrite each inequality in the system

2x + y ≥

1 ➞ y ≥

1 - 2x

so that the left-hand side is y :

x 2 + y ≤

1 ➞ y ≤

1 - x 2

2Enter y = 1 - 2x for Y1 and y = 1 - x 2 for Y2.

Y= 1

1 —

— 2 X//T/n

X//T/n x2

ENTER

3Access the set shade screen

2nd F DRAW G

4Shade the points of y -value so that Y1 ≤ y ≤ Y2.

2nd F VARS A ENTER A 1

2nd F VARS ENTER 2

5Graph the system and find the intersections.

GRAPH

2nd F CALC 2 2nd F CALC 2

6Solve the system.

The intersections are (0, 1) and (2, -3)

The solution is 0 ≤ x ≤ 2.

Graphical solution methods not only offer instructive visualization of the solution process, but they can be applied to inequalities that are often difficult to solve algebraically. The EL-9900 allows the solution region to be indicated visually using the Shade feature. Also, the points of intersection can be obtained easily.

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