The SIMULT Menu

The SIMULT Menu is used to solve a system of n linear equations with n unknowns (up to 30).

Example 1: Find the solution to the following system of linear equations:
2x + 3y = 8
4x - 6y = -8

The values needed to solve the system of equtations are the number of equations and the coefficients in each of the equations. The initial screen prompts for the number of equations:

SIMULT
Number=2 (we type two and press enter since the number of equations is 2)

The display now prompts us to enter the coefficients of the first equation by displaying:

a1,1x1+...+a1,2x2=b1 (representing a_1,1x₁ + a_1,2x₂ = b₁)
The x1 represents the x variable in our problem and x2 is representing the y variable. Below this it prompts for each coefficient:
a1,1=2
a1,2=3
b1= 8

We type in the coefficents of the first equation and press the down arrow or the enter key after each to move to the next one in the list. Missing terms in the equation would have a coefficient of 0. We repeat this for the second equation by pressing the enter key. The display now prompts us to enter the coefficeents of the second equation by displaying:

a2,1x1+...+a2,2x2=b2 (representing a_2,1x₁ + a_2,2x₂ = b₂)
Note the only difference is the subscripts 2 representing the second equation. Then it prompts for each coefficient of the second equation. Be sure to use the (-) key when entering negative coefficients.
a2,1=4
a2,2= -6
b2= -8

Now we press F5 to SOLVE for the simultanious solution to these two equations. The display shows the answer:
x1= 1
x2= 2

That is x=1 and y=2 is a solution to both equations (i.e. is the point of intersection of the two lines). The graph below shows that the two linear equations intersect at the point (1, 2). This can also be checked algebraicly by substituting x=1 and y=2 into the two equations to make sure the point satisfies both of them.

PUT GRAPH HERE

Enter number of equations and coefficients of each equation as before:
SIMULT
Number=3

a1,1=1
a1,2=2
a1,3= -1
b1=4

a2,1=2
a2,2= -3
a2,3=2
b2=7

a3,1=3
a3,2=0 (since there is no y term in the third equation)
a3,3=5
b3=2

Now we press F5 to SOLVE for the roots. The display shows the solution :

x1=4 (for the varible x)
x2= -1 (for the variable y)
x3= -2 (for the variable z)

Example 3: Find the solution to the following system:
x + y = 2
2x + 2y = 2

This system has no solutions (parallel lines). The calculator will give the following error message "ERROR 03 SINGULAR MAT".

Example 4: Find the solutions to the following system:
x + y = 2
2x + 2y = 4

This system has an infinite number of solutions (the lines are actually the the same line). The calculator will give the same error message "ERROR 03 SINGULAR MAT" as we get in Example 3.