This document contains examples of solving systems of equations word problems. It begins with a warm-up problem about a math test worth a total of 63 points made up of 2-point and 3-point problems. Then it provides steps for solving systems of equations, including labeling variables, writing equations, solving, and checking. Finally, it applies these steps to two word problems, one about movie tickets and one about flowers for Valentine's Day.

1.  Warm-Up: Sytstems of
Equations Word Problems
 Reminders:
 Khan Academy
 CW 4.1 - 4.2 Due Monday

2. 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.

3. 1. Mark
the text.
2. Label
variables.
3. Create
equations.
4. Solve.
5. Check.
A restaurant charged one customer $28.20 for
3 small dishes and 5 large dishes and charged
another customer $23.30 for 4 small dishes
and 3 large dishes. What will 2 small and 4
large dishes cost?

5. 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:

6. Applying Systems of Equations:
Mrs. Smith took her family and friends to the movies.
There were a total of 12 people. Children tickets cost $5 and
adult tickets cost $10. She spent a total of $95. How many
adults & how many children went to the movies?

7. For Valentines Day 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