System of Two-Variable Inequalities
The solution region of a system of
Example
Solve a system of
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 A * (
ENTER 2nd F
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Step & Key Operation | Display | Notes |
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*Use either pen touch or cursor to operate. |
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1Rewrite each inequality in the system so that the
2Enter y = 1 - 2x for Y1 and y = 1 - x 2 for Y2.
Y= 1 — 2 X//T/n ENTER *
1 — X//T/n x 2
3Access the set shade screen
2nd F DRAW G *
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4Shade the points of y
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5Graph the system and find the intersections.
GRAPH
2nd F CALC 2 * 2nd F CALC 2 *
6Solve the system.
2x + y ≥ 1 ➞ y ≥ 1 - 2x x 2 + y ≤ 1 ➞ y ≤ 1 - x 2
The intersections are (0, 1) and (2,
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