How do you solve a system of linear equations by using a table?

How do you solve a system of linear equations by using a

table?For example, how can you make two

kinds of polygons using an exact number of magnetic bars?

In this lesson you will learn how to represent solutions and constraints to systems of linear

equations by using a table.

Let’s ReviewYou can make a table to model a

problem.My 50gram pet mouse is growing by 3 grams per day. How much will she weigh in 4

days?

Days Grams0 501 532 563 594 62

In four days she will weigh 62 grams.

Let’s ReviewThe solution to a system of equations is

a set of values that makes both equations true.

5x – 4y = -3y = -3x + 5

x = 1, y = 2

A Common Mistake

Solving for only one of the variables

5x – 4y = -3y = -3x + 5

x = 1

A Common Mistake

Satisfying only one of the constraints

3 pumpkins and an apple costs $3.80. 3

pumpkins and 2 apples costs $5.20.

A pumpkin probably costs $1.00 and an apple costs $0.80. That works in the

first problem.

$3.80$5.20

Core Lesson

A magnetic construction set has 38 bars.

Make a total of 7 regular polygons. The polygons can either be pentagons or

hexagonsUse all of the bars

Core LessonHow can I make a total of 7 shapes?

Polygons MadePentagons Hexagons0 71 62 53 44 35 26 17 0

Bars UsedPentagons Hexagons Total

How can I use exactly 38 bars?

0 42 425 36 4110 30 4015 24 3920 18 3825 12 3730 6 3635 0 35

In this lesson you have learned how to represent solutions and constraints to systems of linear

equations by using a table.

Guided Practice

I have a total of 30 coins, all in nickels and dimes. The coins are worth $2.15 total. How many of each type of coin do I have?

Extension Activities

Look through advertisements to find the price of one type of hat and one type of gloves. Write a problem to say how much money you have spent by buying a certain number of hats and gloves at that price. Trade your problem with a friend. See if your friend can solve your problem!

Extension Activities

Take the problem we worked on in the lesson, but this time allow yourself to find pentagons, hexagons, and triangles. Is there still only 1 solution? Why might the number of solutions not be exactly 1?

Quick Quiz

There are a total of 10 animals in a farmhouse. Some are pigs, and some are ducks. There are 36 legs in all. How many of each animal are there?

A father is 26 years older than his daughter. In 4 years, the father will be 2 more than 5 times her age. Find each of their ages.