Lesson 6: Writing and Graphing Systems of Linear Equations (Alg1.2.12)

Author:Brenda Jiménez, IM Algebra 1, Geometry, Algebra 2 , GeoGebra Classroom Activities

Math Talk

What do you notice? What do you wonder?

A club is selling snacks at a track meet. Oranges cost $1 each and protein bars cost $4 each. They sell a total of 100 items, and collect $304.

Graph Analysis

Match the pair of graphs to a situation.

Select all that apply

A
A restaurant has a total of 20 tables—round tables that seat 2 people and rectangular tables that seat 4 people. All 70 seats in the restaurant are occupied.
B
A family buys a total of 32 tickets at a carnival. Ride tickets cost $1.50 each and food tickets cost $3.25 each. The family pays a total of $90 for the tickets.
C
Tyler and Andre are shopping for snacks in bulk at the grocery store. Tyler pays $10 for 6 ounces of almonds and 8 ounces of raisins. Andre pays $12 for 10 ounces of almonds and 5 ounces of raisins.

Check my answer (3)

Match the pair of graphs to a situation.

Select all that apply

A
A restaurant has a total of 20 tables—round tables that seat 2 people and rectangular tables that seat 4 people. All 70 seats in the restaurant are occupied.
B
A family buys a total of 32 tickets at a carnival. Ride tickets cost $1.50 each and food tickets cost $3.25 each. The family pays a total of $90 for the tickets.
C
Tyler and Andre are shopping for snacks in bulk at the grocery store. Tyler pays $10 for 6 ounces of almonds and 8 ounces of raisins. Andre pays $12 for 10 ounces of almonds and 5 ounces of raisins.

Check my answer (3)

Match the pair of graphs to a situation.

Select all that apply

A
A restaurant has a total of 20 tables—round tables that seat 2 people and rectangular tables that seat 4 people. All 70 seats in the restaurant are occupied.
B
A family buys a total of 32 tickets at a carnival. Ride tickets cost $1.50 each and food tickets cost $3.25 each. The family pays a total of $90 for the tickets.
C
Tyler and Andre are shopping for snacks in bulk at the grocery store. Tyler pays $10 for 6 ounces of almonds and 8 ounces of raisins. Andre pays $12 for 10 ounces of almonds and 5 ounces of raisins.

Check my answer (3)

A Possible Mix?

Diego bought some raisins and walnuts to make trail mix.

Raisins cost $4 a pound and walnuts cost $8 a pound. Diego spent $15 on both ingredients. Decide if each pair of values could be a combination of raisins and walnuts that Diego bought.

4 pounds of raisins and 2 pounds of walnuts

1 pound of raisins and 1.5 pounds of walnuts

2.25 pounds of raisins and 0.75 pounds of walnuts

Here is a situation you saw earlier: Diego bought some raisins and walnuts to make trail mix. Raisins cost $4 a pound and walnuts cost $8 a pound. Diego spent $15 on both ingredients.

Write an equation to represent this constraint. Let be the pounds of raisins and be the pounds of walnuts.

Graph the equation.

Complete the table with the amount of one ingredient Diego could have bought given the other. Be prepared to explain or show your reasoning.

Here is a new piece of information: Diego bought a total of 2 pounds of raisins and walnuts combined.

Write an equation to represent this new constraint. Let be the pounds of raisins and be the pounds of walnuts.

Graph the equation.

Complete the table with the amount of one ingredient Diego could have bought given the other. Be prepared to explain or show your reasoning.

Diego spent $15 and bought exactly 2 pounds of raisins and walnuts.

How many pounds of each did he buy? Explain or show how you know.

Are you ready for more?

For each situation, write a system of equations that represent the constraints (do not solve it).

A dining hall had a total of 25 tables—some long rectangular tables and some round ones. Long tables can seat 8 people. Round tables can seat 6 people. On a busy evening, all 190 seats at the tables are occupied. How many long tables, , and how many round tables,, are there?

A family bought a total of 16 adult and child tickets to a magic show. Adult tickets are $10.50 each and child tickets are $7.50 each. The family paid a total of $141. How many of adult tickets, , and child tickets, , did they buy?

Lesson 6: Writing and Graphing Systems of Linear Equations (Alg1.2.12)

What do you notice? What do you wonder?

Match the pair of graphs to a situation.

Match the pair of graphs to a situation.

Match the pair of graphs to a situation.

Diego bought some raisins and walnuts to make trail mix.

Here is a situation you saw earlier: Diego bought some raisins and walnuts to make trail mix. Raisins cost $4 a pound and walnuts cost $8 a pound. Diego spent $15 on both ingredients.

Graph the equation.

Complete the table with the amount of one ingredient Diego could have bought given the other. Be prepared to explain or show your reasoning.

Here is a new piece of information: Diego bought a total of 2 pounds of raisins and walnuts combined.

Graph the equation.

Complete the table with the amount of one ingredient Diego could have bought given the other. Be prepared to explain or show your reasoning.

Diego spent $15 and bought exactly 2 pounds of raisins and walnuts.

For each situation, write a system of equations that represent the constraints (do not solve it).

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