Simultaneous Equations

MET 107
Homework 21 – Simultaneous Equations
Later in this document, you will be asked to solve a series of simultaneous equations. Pay attention to the
instructions for producing documentation using the Grid and Header and Cell Formulas macros.
Solve each of the systems of equations using matrix math functions in Excel. Whenever a variable is missing
from an equation, its coefficient will be zero in the coefficient matrix. Each problem should be checked by
multiplying the coefficient matrix by the solution matrix to obtain the original constant matrix.
The following is an example (do not turn this in):
.5x 1 - .4x 2 + 3x 4 = 5.2
.8x 1 - 3x 2 + x 3 - .5x 4 = -6.2
x 1 + .4x 2 - .2x 3 + .6x 4 = 4.1
.2x 1 + .6x 2 - .3x 3 = 7.0
Note: Your input region should
list the equations as shown.
You do not have to include the
text boxes.
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Solve the following equations:
A) 2x 1 + 3x 2 = -10
3x 1 - 2x 2 = -2
B) 4x 1 – x 2 – 3x 3 = 1
2x 1 + x 2 + 2x 3 = 5
8x 1 + x 2 - x 3 = 5
Note that A) and B) are to be done on a single worksheet.
Print this worksheet using the both the Grid and Header and the Copy Cell Formula macro.
C) 2x 1 – 3x 2 + x 3 – 2x 4 = 8
x 1 – x 2 - 6x 4 = -4
3x 2 + 4x 4 = 6
6x 1 + 2x 2 – 3x 3 + 7x 4 = 12
Note that C) is to be done on a single worksheet.
Print this worksheet using the both the Grid and Header and the Copy Cell Formula macro.
D) This problem involves solving 10 equations for 10 unknown forces in order to determine the forces in
truss members. F 1 , F 2 , 1 , and 2 should be set up to be variable inputs in your sheet.
Start a new worksheet for this problem.
The equations of equilibrium are as follows:
R 1 + T 1 cos 60° + T 2 = 0
R 2 + T 1 sin 60° = 0
-T 2 – T 3 cos 60° + T 4 cos 60° + T 5 = 0
T 3 sin 60° + T 4 sin 60° = 0
-T 5 – T 6 cos 60° = 0
T 6 sin 60° + R 3 = 0
Hint:
The easiest way of displaying these
equations in Excel would be to use the
Snipping Tool to insert an image of
these.
-T 1 cos 60° + T 3 cos 60° + T 7 – F 1 cos 1 = 0
-T 1 sin 60° – T 3 sin 60° – F 1 sin 1 = The information in these boxes are your
“constants” and are a function of the Inputs
-T 4 cos 60° – T 7 + T 6 cos 60° – F 2 cos 2 = 0
-T 4 sin 60° – T 6 sin 60° – F 2 sin 2 = 0
Note that R 1 is the horizontal reactive force, R 2 is the vertical reactive force at the left support and R 3 is the
vertical reactive force at the right support.
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In Excel, solve the system of equations.
Use a format similar to the one shown below for your calculations.
Draw a figure of the truss and include textboxes to label the figure. Link the textboxes to the results so the
force in each member (T 1 – T 7 ; shown in the boxes) and the reactions (R 1 – R 3 ) are shown in the figure. The
given forces and their angles should also appear in the figure, linked to the input boxes. The solution to the
given problem is shown.
Print your worksheet for the above test case using the both the Grid and Header and the Copy Cell
Formula macro.
Change the input values as follows:
F 1 = 6000 lbs, 1 = 60 deg, F 2 = 2000 lbs, 2 = 90 deg.
Print your worksheet using the both the Grid and Header macro only.
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