3 by 3 Simultaneous Equations Code in C++
To solve 3 by 3 simultaneous equations, we will simply eliminate the z variable, then call out to our simultaneous2unknown code module.
To solve 3 by 3 simultaneous equations, we will simply eliminate the z variable, then call out to our simultaneous2unknown code module.
Consider the equations:
x + 2y - z = 2; and
3x - y + 2z = 4
2x + 3y + 4z = 9
Multiply equations 1, 2 & 3 by the LCM of the coefficients
of variable z, divided by the z coefficient
of the respective equation.
(4/-1) X (x + 2y - z = 2)
⇒
-4x - 8y + 4z = -8
(4/2) X (3x - y + 2z = 4)
⇒
6x - 2y + 4z = 8
(4/4) X (2x + 3y + 4z = 9)
⇒
2x + 3y + 4z = 9
Subtract the new equations obtained in Step 2;
eqn (2) from eqn (1) and eqn (3) from eqn (2).
-4x - 8y + 4z = -8
-
6x - 2y + 4z = 8
⇒
-10x - 6y = -16
6x - 2y + 4z = 8
-
2x + 3y + 4z = 9
⇒
4x - 5y = -1
Call out to our simultaneous2unknown
code module to solve for x and y.
⇒
(x, y) = (1, 1);
Obtain z by solving for z from any of the
original equations, using the found values of x
and y.
x + 2y - z = 2
⇒
1 + 2(1) - z = 2;
⇒
-z = 2 - 3 = -1;
⇒
z = -1/-1 = 1;
Create a new class file;
call it Simultaneous3Unknown.
Type out the adjoining C++ code for solving simultaneous equations with 3 unknowns.
Note: The code module for
finding LCM
has been explained in the Primary Category.
You can comment out the Simultaneous2Unknown C++ object
code in the main class from the previous lesson or simply continue from where it stopped.
Feel free to try out your own set of x_coefficients, y_coefficients, z_coefficients and equals values for 3 by 3 Simultaneous Equations.