Chapter Equation Calculations Your graphic calculator can perform the following three types of calculations: • Linear equations with two to six unknowns • High-order equations (quadratic, cubic) • Solve calculations 7-1 7-2 7-3 7-4 7-5 Before Beginning an Equation Calculation Linear Equations with Two to Six Unknowns Quadratic and Cubic Equations Solve Calculations What to Do When an Error Occurs 7
7-1 Before Beginning an Equation Calculation 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. k Entering an Equation Calculation Mode In the Main Menu, select the EQUA icon to enter the Equation Mode. • {SIML} ... {linear equation with two to six unknowns} • {POLY} ... {quadratic or cubic equation} • {SOLV} ... {solve calculation} k Clearing Equation Memories 1.
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,
7-2 Linear Equations with Two to Six Unknowns k Solving 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 1. While in the Linear Equation Mode (SIML), press 2 (3), because the linear equations being solved have three unknowns. 2. Input each coefficient.
Linear Equations with Two to Six Unknowns 7-2 • Internal calculations are performed using a 15-digit mantissa, but results are displayed using a 10-digit mantissa and 2-digit exponent. • This unit performs simultaneous linear equations by placing the coefficients inside of a matrix. Because of this, as the coefficient matrix approaches zero, precision in the inverse matrix is reduced and so precision in the results produced also deteriorates.
7-3 Quadratic and Cubic Equations This calculator can also solve quadratic and cubic equations that match the following formats (when a G 0): • Quadratic: ax2 + bx + c = 0 • Cubic: ax3 + bx2 + cx + d = 0 k Specifying the Degree of an Equation While in the Equation Mode, press 2 (POLY) and then specify the degree of the equation. • {2}/{3} ... {quadratic}/{cubic} equation k Solving a Quadratic or Cubic Equation Example To solve the following cubic equation: x3 – 2 x 2 – x + 2 = 0 1.
Quadratic and Cubic Equations 7-3 • Internal calculations are performed using a 15-digit mantissa, but results are displayed using a 10-digit mantissa and 2-digit exponent. • An error occurs whenever the unit is unable to solve the equations. • Pressing 1 (REPT) returns to the initial display of the Cubic Equation Mode. k Multiple root (1 or 2) solutions or imaginary number solutions The following examples illustrate how multiple-root solutions and imaginary number solutions are handled.
7-3 Quadratic and Cubic Equations k Changing Coefficients You can change a coefficient either before or after you register it by pressing w. uTo change a coefficient before registering it with w Press the A key to clear the current value and then input another one. uTo change a coefficient after registering it with w 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.
7-4 Solve Calculations You can determine the value of any variable you are using without having to solve the equation. Input the equation, and a table of variables appears on the display. Use the table to assign values to variables and then execute the calculation to obtain a solution and display the value of the unknown variable. P.394 • You cannot use the variable table in the Program Mode.
7-4 Solve Calculations 3. Input the values. bew(H=14) aw(V=0) cw(T=2) j.iw (G=9.8) 4. Press f to move the highlighting to V = 0. 5. Press 6 (SOLV) to obtain the solution. Equation Solution • An error occurs if you input more than one equals sign. • “Lft” and “Rgt” indicate the left and right sides that are calculated using the approximate value. The closer the difference between these two values is to zero, the greater the accuracy of the result.
Solve Calculations 7-4 • Solve uses Newton’s method to calculate approximations. The following can sometimes occur when this method is used. —Solutions may be impossible to obtain for certain initial estimated values. Should this happen, try inputting another value that you assume to be in the vicinity of the solution and perform the calculation again. —The calculator may be unable to obtain a solution, even though a solution exists.
7-5 What to Do When an Error Occurs uError during coefficient value input Press the A key 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 A key to clear the error and display coefficient a. Try inputting values for the coefficients again.
