Equation Calculations (EQN)

You can use the following procedure in the EQN Mode to solve simultaneous linear equations with two or three unknowns, quadratic equations, and cubic equations.

1. Press (EQN) to enter the EQN Mode.

2. On the menu that appears, select an equation type.

To select this calculation type:	Press this key:
Simultaneous linear equations with two unknowns	(anX + bnY = cn)
Simultaneous linear equations with three unknowns	(anX + bnY + cnZ = dn)
Quadratic equation	(aX2 + bX + c = 0)
Cubic equation	(aX3 + bX2 + cX + d = 0)

3. Use the Coefficient Editor that appears to input coefficient values.

To solve 2x2 + x - 3 = 0, for example, press in step 2, and then input the following for the coefficients (a = 2, b = 1, c = -3): 213.

To change a coefficient value you already have input, move the cursor to the appropriate cell, input the new value, and then press .

Pressing will clear all of the coefficients to zero.

Important!

The following operations are not supported by the Coefficient Editor: , (M-), (STO). Pol, Rec, ÷R, and multi-statements also cannot be input with the Coefficient Editor.

4. After all the values are the way you want, press .

This will display a solution. Each press of will display another solution. Pressing while the final solution is displayed will return to the Coefficient Editor.

You can scroll between the solutions using the and keys.

To return to the Coefficient Editor while any solution is displayed, press .

Note

Even if Natural Display is selected, the solutions of simultaneous linear equations are not displayed using any form that includes √ .

Values cannot be converted to engineering notation on the solution screen.

A message appears to let you know when there is no solution or when there are infinite solutions. Pressing or will return to the Coefficient Editor.

Changing the Current Equation Type Setting

Press (EQN) and then select an equation type from the menu that appears. Changing the equation type causes the values of all Coefficient Editor coefficients to change to zero.

EQN Mode Calculation Examples

Example 1: x + 2y = 3, 2x + 3y = 4

(EQN)(anX + bnY = cn)
123
234

(X=) -1

(Y=) 2

Example 2: x - y + z = 2, x + y - z = 0, -x + y + z = 4

(EQN)(anX + bnY + cnZ = dn)
1112
1110
1114

(X=) 1

(Y=) 2

(Z=) 3

Example 3: 2x2 - 3x - 6 = 0 (MthIO-MathO)

(EQN)(aX2 + bX + c = 0)
236
(X1=) ^{3 + √57}₄

(X2=) ^{3 - √57}₄

(X-Value Minimum=)* ³₄

(Y-Value Minimum=)* - ⁵⁷₈

* The local minimum value is displayed when a > 0. The local maximum value is displayed when a < 0.

Example 4: x2 - 2√2x + 2 = 0 (MthIO-MathO)

(EQN)(aX2 + bX + c = 0)
1222
(X=) √2

Example 5: x3 - 2x2 - x + 2 = 0

(EQN)(aX3 + bX2 + cX + d = 0)
1212
(X1=) -1

(X2=) 2

(X3=) 1

CASIO

fx-115ES PLUS
fx-991ES PLUS C
(2nd edition / NATURAL-V.P.A.M.)

Before Using the Calculator

Calculation Modes and Calculator Setup

Inputting Expressions and Values

Basic Calculations

Function Calculations

Using Calculation Modes

Technical Information

Frequently Asked Questions