Algebra 1 Unit 4 – Bellwork
Bellwork #1
1. List four possible solutions of the two-variable equation: x + 2y = 20.
2. List four possible solutions of the two-variable equation: y = 2x – 5.
Bellwork #2
1. What exactly is a system of equations?
2. How can you tell if a system of equations has a unique solution?
3. The solution of a system of linear equations can be found by looking at where their graphs
intersect. But what does it mean when the lines never intersect? What sort of lines never
intersect?
4. Draw graphs to solve the following system of equations. Write your solutions as an ordered pair.
1
𝑦 = 2𝑥 −4
a. {
3
𝑦 = 4𝑥 −5
Bellwork #3
1. Write the following statement as a mathematical inequality: The cost of a car rental (y) is at least
$15 times the number of days (x) plus the flat rate of $28.
2. How can you tell where the solutions to a two-variable inequality are on a graph?
3. Graph the following system of linear inequalities.
1
𝑦 > 3𝑥 − 1
{
2
𝑦 ≤ −3𝑥 + 4
4. Tell whether the following points are solutions to the system of linear inequalities above.
a. (-1, 3)
b. (4, 5)
c. (0, 0)
d. (1,4)
Bellwork #4
1. Explain the process of “Substitution” in solving a system of two linear equations.
2. How can you get a system of equations that has no solutions?
3. How can you get a system of equations that has infinitely many solutions?
4. Use substitution to solve the following systems. Where necessary, leave answers as simplified
fractions – not decimals.
𝑦 = 3𝑥 + 1
a. {
2𝑥 + 4𝑦 = 6
Bellwork #5
1. When is it a good idea to use the “Elimination Method” for solving a system of two linear equations
instead of the “Substitution Method”.
2. Explain the four different types of examples given in the notes for solving systems of equations
with elimination.
3. In using the “Elimination Method”, what do you do once you have solved for one of the variables
and now need to solve for the other?
4. Use the “Elimination Method” to solve the following systems:
3𝑥 + 2𝑦 = 1
a. {
−4𝑥 − 4𝑦 = 8
Bellwork #6
1. Solve the following system of three linear inequalities:
10𝑥 + 5𝑦 + 20𝑧 = −14
{ 9𝑥 − 𝑦 + 10𝑧 = −4
5𝑥 − 4𝑦 − 10𝑧 = 0
Bellwork #7
1. Quick Use Disposable Phones charges $30 to buy a disposable cell phone and then charges $0.30
for each minute used on the cell phone. Tossable Tellies, a competing company charges $54 to buy
a disposable cell phone and then $.06 for each minute used on the cell phone.
a. The graph below models the cell phone plans. Explain what each of the lines represent.
b. At what number of minutes will the two companies charge the exact same amount?
c. If you are going to use your disposable phone for exactly 1.5 hours, which company should
you choose?
d. If you are going to use your phone for 2 hours or more, which company should you choose?
Practice 4.6
1. Explain one of the hints you can look for in a word problem to tell that it is a system of equations
word problem.
2. Write the following sentence as a mathematical equation: The sum of the number of elephants (x)
plus the number of ostriches (y) gathered at a watering hole is 19.
3. Write this scenario as a mathematical equation: All the elephants (x) at the watering hole have
four legs each and all of the ostriches (y) at the watering hole have two legs each. Between the two
types of creatures, there are 62 legs at the watering hole.
4. Solve the system of equations formed by problems 2 and 3 to determine how many of each type of
animal is at the watering hole.
5. In a change purse there are only nickels and dimes. Altogether there are 42 coins in the purse
totaling $3.05. Find how many nickels and how many dimes there are in the purse.
6. Invent your own story problem that would require a system of two equations in order to solve it.
Solve your problem for both variables.