This document contains a daily agenda and warm-up problems for math class including: 1) Solving systems of equations by graphing, substitution, and elimination. Example problems include solving for costs of flowers and costs of different internet providers over time. 2) Review of fractions, inequalities, and solving multi-step equations. 3) An example of solving a 3x3 system of equations by eliminating a variable and substituting values. 4) Warm-up questions ask students to write and solve systems of equations modeling real-world scenarios like costs of soccer equipment and costs of fitness clubs over time.

1. Today:
 Warm-Up: Old & New
 New Type of Systems Problem
 Intro. to Systems of Inequalities
 CW 4.1 - 4.2 due as of last Friday
 Last day for Khan Academy is
Tomorrow
 CW 4.3 Distributed Tomorrow
4/04/16

2. The pie chart below shows how the average family spends
their money while on vacation.
If a family spent
$3000 while on
vacation, how much
was spent on gas?
What simplified fraction of the cost is spent on food and
entertainment?
Warm-Up: Review Questions

3. 12
3
2
 xy
4
3
4
1
 xy
What is y when x = -18
What is y when x = -6
Warm-Up: Review Questions

4. Is the system consistent or
inconsistent?
Is the system dependent or
independent?
Write the systems of equations
shown on the graph.
Warm-Up: Systems of Equations

5. For her birthday,Mark bought his mom 12 flowers, a
mixture of roses and daisies. The roses cost $1.15 each
and the daisies cost $1.35 each. If he spent $16.00, how
many daisies did he buy?
x =
y =
# of
roses
# of
daisies
12x y 
1.15 1.35 16.00x y 
 100  100  100
115x 135y 1600
115x
12x y 
  12x  11
11 11 
1x 
11 daisies
1. Mark
the text.
2. Label
variables.
3. Create
equations.
4. Solve.
5. Check.
 115  115  115
115y 1380 
20 20
11y 
20 220y 
Let’s eliminate
the ‘x’
Try solving by elimination
Warm-Up: Systems of Equations

6. A math test has a total of 25 problems. Some problems are
worth 2 points and some are worth 3 points. The whole test
is worth 63 points. How many 2-point problems were there?
x =
y =
# of 2-point
problems
# of 3-point
problems
25x y 
2 3 63x y 
 2  2  2
13y 
2x 2y 50 
2 3 63x y 
25x y 
  25x  13
13 13 
12x 
12 2-point problems
1. Mark
the text.
2. Label
variables.
3. Create
equations.
4. Solve.
5. Check.

7. Solving 3x3 Systems:(1)
The graph of the solution set of an equation in three
variables is a plane, not a line. In fact, graphing equations in
three variables requires the use of a three-dimensional
coordinate system. It is therefore, not practical to solve
3x3 systems by graphing
Solve the System: 4x + 2y - z = -5
3y + z = -1
2z = 10
1. Which is the easiest
variable to solve for?
2. Plug in where and solve
for what?
3. Substitute y and z values into equation 1; solve for x.
4. Substitute all values, check for equality.
5. The solution set is (1, -2, 5)
Solving 3x3 Systems:

8. A sporting goods store is having a sale on soccer equipment. One
coach buys 10 soccer balls and 2 ball bags $155. Another coach
buys 12 soccer balls and 3 ball bags for $189.
What is the cost of each item?
Write the equations and determine the best method for solving.
Last warm-Up Question
Write the equations and determine the best method for solving.

10. Many systems questions ask you to compare the costs of two
different businesses like fitness clubs, car rentals, home repair,
and then determine after how many months, miles, or hours, the
costs will be the same.
This question is asking after how many months will the cost be
the same for both companies. Even though these are not solved
by graphing, we still must determine the independent and
dependent variables. The cost depends on the number of months
used. The cost for Interwebs is.....
What is the slope-intercept form of both equations?

11. After writing the two
equations, what method
is best for solving?
y - 21.95x = 10
y - 22.45x = 0
1. Use elimination to solve for 'x', which is the number of
months until the costs are equal.
.5x = 10 x = 20
If you're only going to use an internet service for one year,
which company would you choose?
What is the cost for both companies after 20 months?
2. Use substitution to solve for 'x', which is the number of
months until the costs are equal.

12. What are the independent and dependent variables?
Write the two equations and solve
Write costs for both companies in slope intercept form.
Rearrange into standard form.