Download Solving System Of 3 Equations On Calculator

Math 1215 How to Solve a System of Three Equations on Your TI83/84 Calculator
Since the quarter is ending too soon and we don’t get to study matrices (too bad!), I will just show you
how to solve a system of equations on your calculator using a matrix, without too much explanation.
That way you can check your algebraic solutions to the homework or test problems.
Example #1: Solve this system of equations on your calculator:
x + y + z = 10
x – y + 2z = 9
5x + y + z = 30
First of all, be sure that your system is in a nice order, with the variables all lined up. The “array” you’ll
be entering in for the system above is:
1 1 1 10
1 -1 2 9
5 1 1 30
Steps:
1. Access the MATRIX feature using your 2nd key . (It is the key below your MATH key.) Arrow over
to EDIT and hit ENTER.
2. For a system of 3 equations you need a 3x4 matrix, so enter that in the top line.
Note that it is not able to show all 4 columns at once.
3. Now enter in your array of numbers as listed above, hitting ENTER each time to get to the next
spot.
4. When you’re done your screen will look like this:
5. Now go to the HOME screen again by hitting 2nd QUIT. You need to get to the MATRIX menu
now so hit 2nd MATRIX. This time you arrow over once to MATH. Scroll way down to option B,
which is RREF( and hit ENTER.
6. Finally, tell the calculator you want it to solve Matrix A by hitting 2nd MATRIX 1 and ENTER.
7. Read off the answers from the last column: x = 5, y = 2, z = 3
Example #2: Now suppose you want to solve this word problem:
A $92,000 trust is to be invested in bonds paying 9%, CD’s paying 6% and mortgages paying 10%. The
bond plus the CD investment must equal the mortgage investment. To earn a $8200 annual income
from the investments, how much should the bank invest in bonds?
First write a system:
B + C + M = 92000 (a statement about the amounts invested)
B+C=M
(the second sentence translated)
0.09B + 0.06C + 0.10M = 8200 (a statement about the interest earned)
To solve this on your calculator you must first rearrange the 2nd equation so it is B + C – M = 0. Then
enter the array:
1
1
1 92000
1
1 -1 0
.09 .06 .10 8200
The answers are: Bonds = $28,000 , CD’s = $18,000 , Mortgages = $46,000.