Casio FX-9750G User manual

Equation Calculations

Your graphic calculator can solve the following three types of equa-

tions:

•Linear equations with two to six unknowns

•Quadratic equations

•Cubic equations

7-1 Before Beginning an Equation Calculation

7-2 Linear Equations with Two to Six Unknowns

7-3 Quadratic and Cubic Equations

7-4 What to Do When an Error Occurs

Chapter

116

7-1 Before Beginning an Equation Calculations

Before beginning an equation calculation you have to first enter the correct mode,

and you must also clear the equation memories of any data that might be left over

from a previous calculation.

kEntering an Equation Calculation Mode

Highlight the EQUA icon on the Main Menu and then press w.

1(SIML) ....... Linear equation with two to six unknowns

2(POLY) ...... Quadratic or cubic equation

kClearing Equation Memories

After entering an equation calculation mode (SIML or POLY), clear the calculation

memory for that mode. In the case of SIML, use the function keys to specify the

number of unknowns, from two (1) to six (5). In the case of POLY, use the func-

tion keys to specify either two (1) or three (2) polynomials.

2(DEL)

Press 1(YES) to clear the equation memories of that mode (SIML or POLY), or

6(NO) to abort the clear operation without clearing anything.

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117

7-2 Linear Equations with Two to Six Unknowns

You can use the procedures described here to solve linear equations with unknowns

that match the following formats:

Two unknowns a1x + b1y = c1

a2x + b2y = c2

Six unknowns a1x + b1y + c1z + d1t + e1u + f1v = g1

a2x + b2y + c2z + d2t + e2u + f2v = g2

a3x + b3y + c3z + d3t + e3u + f3v = g3

a4x + b4y + c4z + d4t + e4u + f4v = g4

a5x + b5y + c5z + d5t + e5u + f5v = g5

a6x + b6y + c6z + d6t + e6u + f6v = g6

• You can also solve linear equations with three, four, and five unknowns. In each

case, the format is similar to those shown above.

kEntering the Linear Equation Mode for Two to Six

Unknowns

While the Equation Mode is displayed, press 1(SIML).

1(SIML)

1(2) ............. Linear equation with two unknowns

2(3) ............. Linear equation with three unknowns

3(4) ............. Linear equation with four unknowns

4(5) ............. Linear equation with five unknowns

5(6) ............. Linear equation with six unknowns

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118

kSolving Linear Equations with Three Unknowns

Example To solve the following linear equations for x, y, and z:

4x+y–2z=–1

x+6y+3z=1

–5x+4y+z=–7

While in the Linear Equation Mode (SIML), press 2(3), because the linear equa-

tions being solved have three unknowns.

2(3)

Input each coefficient.

ewbw-cw

-bw

bwgwdwbw

-fwewbw

-hw

Each time you press w, the input value is registered in the highlighted cell. Each

press of winputs values in the following sequence:

coefficient a1→coefficient b1→coefficient c1→coefficient d1→

coefficient a2→coefficient b2→coefficient c2→coefficient d2→

coefficient a3→coefficient b3→coefficient c3→coefficient d3

• You can input fractions and value memory contents as coefficients.

After inputting the coefficients, solve the equations.

1(SOLV)

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7 - 2 Linear Equations with Two to Six Unknowns

Highlighted solution cell value

Value being input into highlighted cell

Coefficient input cells

119

• Internal calculations are performed using a 15-digit mantissa, but results are dis-

played using a 10-digit mantissa and 2-digit exponent.

• This unit performs simultaneous linear equations by placing the coefficients in-

side of a matrix. Because of this, as the coefficient matrix approaches zero, pre-

cision in the inverse matrix is reduced and so precision in the results produced

also deteriorates. For example, the solution for a linear equation with three un-

knowns would be calculated as shown below.

xa1b1c1

–1 d1

y=a2b2c2d2

za3b3c3d3

• An “Ma ERROR” occurs whenever the unit is unable to solve the equations.

• Pressing 1(REPT) returns to the initial display of the Linear Equation Mode.

Depending on the coefficients that you use, it may take considerable time for

the calculation result of simultaneous linear equations to appear on the dis-

play. Failure of a result to appear immediately does not mean that the unit is

not functioning properly.

kChanging Coefficients

You can change a coefficient either before or after you register it by pressing w.

uTo change a coefficient before registering it with ww

Press the Akey to clear the current value and then input another one.

uTo change a coefficient after registering it with ww

Use the cursor keys to highlight the cell that contains the coefficient that you want to

change. Next, input the value that you want to change to.

kClearing All the Coefficients

While in the Linear Equation Mode, press the 3(CLR) function key. This operation

clears all the coefficients to zero.

3(CLR)

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Linear Equations with Two to Six Unknowns 7 - 2

120

7-3 Quadratic and Cubic Equations

This calculator can also solve quadratic and cubic equations that match the following

formats (when aGG

G0):

• Quadratic: ax2+ bx + c= 0

• Cubic: ax3+ bx2+ cx + d= 0

kEntering the Quadratic/Cubic Equation Mode

While in the Equation Mode, press 2(POLY).

2(POLY)

1(2) ............. Quadratic equation

2(3) ............. Cubic equation

kSolving a Quadratic or Cubic Equation

Example To solve the following cubic equation:

x3– 2x2– x+ 2 = 0

Press 2(3) to enter the Cubic Equation Mode.

2(3)

Input each coefficient.

bw-cw

-bwcw

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Value being input into highlighted cell

Cell for input of coefficients

121

• Each time you press w, the input value is registered in the highlighted cell. Each

press of winputs values in the following sequence:

coefficient a→coefficient b→coefficient c→coefficient d

Input for coefficient dis required only for cubic equations.

• You can input fractions and value memory contents as coefficients.

After inputting the coefficients, press 1(SOLV) to solve the equations.

1(SOLV)

• Internal calculations are performed using a 15-digit mantissa, but results are dis-

played using a 10-digit mantissa and 2-digit exponent.

• An “Ma ERROR” occurs whenever the unit is unable to solve the equations.

• Pressing 1(REPT) returns to the initial display of the Cubic Equation Mode.

kQuadratic equations that produce multiple root (1 or 2)

solutions or imaginary number solutions

The following examples illustrate how multiple-root solutions and imaginary number

solutions are handled.

uTo solve a cubic equation that produces a multiple-value solution

Example To solve the following cubic equation:

x3– 4x2+ 5x– 2 = 0

bw-ewfw-cw

1(SOLV)

Quadratic and Cubic Equations 7 - 3

Highlighted solution cell value

122

uTo solve a cubic equation that produces an imaginary number

solution

Example To solve the following cubic equation:

x3+ x2+ x– 3 = 0

bwbwbw-dw

1(SOLV)

It may take considerable time for the calculation result of cubic equations to

appear on the display. Failure of a result to appear immediately does not mean

that the unit is not functioning properly.

kChanging Coefficients

You can change a coefficient either before or after you register it by pressing w.

uTo change a coefficient before registering it with ww

Press the Akey to clear the current value and then input another one.

uTo change a coefficient after registering it with ww

Use the cursor keys to highlight the cell that contains the coefficient that you want to

change. Next, input the value that you want to change to.

kClearing All the Coefficients

While in the Quadratic or Cubic Equation Mode, press the 3(CLR) function key.

This operation clears all the coefficients to zero.

3(CLR)

7 - 3 Quadratic and Cubic Equations

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123

7-4 What to Do When an Error Occurs

uError during coefficient value input

Press the Akey to clear the error and return to the value that was registered for the

coefficient before you input the value that generated the error.Try inputting a new

value again.

uError during calculation

Press the Akey to clear the error and display coefficient a. Try inputting values for

the coefficients again.

• Note that even when you press the Akey, the values assigned for coefficients

are retained.

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