System Of Two-Variable Inequalities - Sharp EL9600C - Graphing Calculator Handbook

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
2
x + y 1
Before There may be differences in the results of calculations and graph plotting depending on the setting.
Start
Return all settings to the default value or to delete all data.
Set the zoom to the decimal window:
Step & Key Operation
(When using EL-9600)
*Use either pen touch or cursor to operate.
1
Rewrite each inequality in the system
so that the left-hand-side is y :
2
Enter y = 1 - 2x for Y1 and y = 1 - x
for Y2.
—
Y= 1 2
n
—
1 x
X/ /T/
Access the set shade screen
3
G
2nd F DRAW
*
1
*
4 Shade the points of y -value so that
Y1 y Y2.
— —
* *
5
Graph the system and find the
intersections.
GRAPH
2
2nd F CALC 2nd F
*
6
Solve the system.
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-
9600/9400 allows the solution region to be indicated visually using the Shade feature. Also,
the points of intersection can be obtained easily.
(
A
ZOOM
*
(When using EL-9600)
2
n
ENTER
X/ /T/
*
2
—
*
2
CALC
*
EL-9600/9400 Graphing Calculator
)
7
ENTER 2nd F
*
Display
2x + y
2
x + y
The intersections are (0, 1)
and (2, -3)
The solution is 0
Notes
1 y 1 - 2x
2
1 y 1 - x
x 2.
7-3