Solving Systems of Linear Equations ▪ Page 1 of 8
Name: _____________________________________________
Serafino ▪ Algebra II
2C:2
1.
Per: _________
Date: __________________
Solving
3x3 Systems (x, y, z)
3.2
Using substitution & elimination
First, let’s solve 3x3 Systems of Equations with Substitution
a.
x – 2y + 3z = –4
y–z=3
z = –1
c.
x + 2y + z = 1
y–z=2
4z = 8
b.
d.
x + 3y = 1
y + 2z = 5
z=3
4x – y + 2z = 6
y + 4z = 2
2z = 4
Solving Systems of Linear Equations ▪ Page 2 of 8
2. Now let’s solve using Elimination:
a.
x+y+z=5
2x – y + z = 4
3x – y + 2z = 8
b.
x+y+z=6
x+y=0
–y + z = 4 – x
Solving Systems of Linear Equations ▪ Page 3 of 8
c.
x + 2y – 3z = –8
2x + y + 3z = 17
x – 3y + 3z = 11
d.
2x + y – z = –7
–2x – y + 3z = 17
2x + 3y – 2z = –12
Solving Systems of Linear Equations ▪ Page 4 of 8
e.
x + 2y – 4z = 2
–x + 2y – 4z = –2
–x – 2y + 4z = –2
f.
2x + 3y – z = 4
4x + 6y – 2z = 6
–2x + y + z = –2
Solving Systems of Linear Equations ▪ Page 5 of 8
Rearrange the equations so they line up for elimination:
g.
3a + b = – c + 7
a + 3b – c = 13
b = 2a – 1
h.
13 = 3x – y
4y – 3x + 2z = –3
z = 2x – 4y
Solving Systems of Linear Equations ▪ Page 6 of 8
3.
Applications of 3x3 systems:
Track Meet: RHS competed in a track meet. They had 20 students won medals in first, second or third place in
various events. First place is worth 5 points, second place is worth 3 points, and third place is worth 1 point.
The students at RHS won total of 68 points. The number of second place finishes was as many as first and third
place combined. How many runners finished in each place?
Taping Shows: For Chrismukkah, you make a tape of your three favorite TV shows for your friend: Family
Guy, Lost, and One Tree Hill. You can completely fill the tape with 7 episodes. You want include twice as many
episodes of Lost as Family Guy. An episode of Family Guy lasts 30 minutes. An episode of Lost and One Tree
Hills lasts 60 minutes. Your VCR tape can only hold 360 minutes of recording. How many episodes of each
show can you tape?
Solving Systems of Linear Equations ▪ Page 7 of 8
Arcade: The local arcade uses 3 different colored tokens for their game machines. For $20, you can buy the
following options of token packages: 14 gold, 20 silver and 24 bronze OR 20 gold, 15 silver and 19 bronze OR
30 gold, 5 silver, 13 bronze. How much is each token worth?
Ridgewood Cinemas: Ridgewood Cinemas sold a total of 8500 tickets, for a total of $64,600. A child ticket
costs $5, a student ticket costs $6 and an adult ticket costs $8.50. They sold twice as many student tickets as child
tickets. How many of each was sold?
Solving Systems of Linear Equations ▪ Page 8 of 8
I’m Lovin’ It: Matt bought McDonald’s for our Algebra II class with all the coupons he’s been receiving. He
ordered 200 items. He ordered Cheesburgers for 1.50 each, Big Macs for $2.60 each, and 20-piece McNuggets
for 5.75... and the order came to $589.50. He ordered 20 fewer McNuggets than Big Macs. How many of
each item was ordered?
Homework: Textbook pg 171: 9 – 25 odd, 29–33 all, 37