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Math 1:
RREF Notes
Name:_________________________________
Date:_________________ Class Pd: _________
RREF (the Lazy Man’s Method)
RREF is a shortcut to _____________________ using the ____________________ ________________________.
Steps to complete RREF in the graphing calculator:
1.) Press
2nd
then
x-1
. This takes us to the matrix menu.
ENTER
2.) Scroll over to EDIT and hit
3.) Type in the dimensions as 2 x 3. Then enter the coefficients and constants in the matrix.
4.) Hit
5.) Hit
2nd
2nd
MODE
then
x-1
. This takes us out of the matrix menu.
to go back to the matrix menu.
6.) Scroll over the MATH option and scroll up or down to option B labeled RREF. Hit
7.) Press
2nd
then
x-1
ENTER
. This takes us to the matrix menu.
8.) Scroll to the letter matrix you entered your numbers in and hit
Your answer should appear as a matrix that looks like [
𝟏
𝟎
ENTER
two times.
𝟎 𝒙
].
𝟏 𝒚
Note: If you do not get a matrix that looks like the one above, your answer is either ________________ or
_________________.
For each system of equations, rewrite it as a matrix. Then solve using RREF.
1) 2𝑥 + 5𝑦 = 1
𝑥−𝑦 =4
2) 4𝑥 + 9𝑦 = 35
−16𝑥 − 36𝑦 = −140
3) 3𝑥 + 2𝑦 = 1
6𝑥 + 4𝑦 = 4
4) 2𝑥 − 5𝑦 = 1
−𝑥 + 4𝑦 = 4
HW: Define the variables, write a system of equations to represent the given scenarios, then solve:
1) A lacrosse coach purchases helmets and shoulder pads for his varsity and JV teams. He buys 20 helmets and
11 sets of shoulder pads for his varsity team and spends $2,220. He purchases 15 helmets and 13 sets of
shoulder pads for the JV team for a total of $1,760. How much did each helmet and set of shoulder pads
cost?
2) Office depot is having a sale on school supplies. Elisa purchased 3 notebooks and 6 packs of pencils for
$13.50. Derek purchased 5 notebooks and 2 packs of pencils for $14.50. How much did each notebook and
pack of pencils cost?
3) The Jones and Tucker family ordered carryout from a diner. The Jones family ordered 5 burgers and 3
chicken sandwiches for $39.50. The Tucker family ordered 2 burgers and 2 chicken sandwiches for $19. How
much does a burger and chicken sandwich cost?
4) Six Flags charges money for a ring toss game and a basketball shot game. Steve spent played the ring toss
game 3 times and the basketball game 3 times for a total of $10.50. Kim played the basketball game 5 times
and the ring toss game once for a total of $11.50. How much did each game cost?
5)
John and Sierra purchased two sizes of bottled water at a store. John bought 2 big bottles and 4 little
bottles that have a total of 40 ounces of water. Sierra bought 5 big bottles and 1 small bottle that have a
total of 64 ounces of water. How many ounces does each bottle hold?
6)
Five adult tickets and 3 senior citizens tickets to King’s Dominion will cost $319.92, while 7 adult and 2
senior citizens tickets will cost $370.91. How much does each adult and each senior citizen’s ticket cost?
7)
DeShawn and Shayna are selling flower bulbs for a school fundraiser. Customers can buy bags of
windflower bulbs and bags of daffodil bulbs. DeShawn sold 10 bags of windflower bulbs and 12 bags of
daffodil bulbs for a total of $380. Shayna sold 6 bags of windflower bulbs and 8 bags of daffodil bulbs for a
total of $244. What is the cost each of one bag of windflower bulbs and one bag of daffodil bulbs?
8)
At a local grocery store, 5 oranges and 14 bananas cost $1.30, whereas 8 oranges and 9 bananas cost $1.41.
Find the cost of each orange and each banana.