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# 2-3-11 - PowerPoint PPT Presentation

2-3-11. Please have hw out to correct. Equations with Two Variables. Lesson 8-2 p.391. Equations with Two Variables. In the other chapters, we learned how to solve equations like this: 5x + 3 = 2x +9 In this type of equation, there was only one kind of variable—”x”.

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2-3-11
• Please have hw out to correct.

### Equations with Two Variables

Lesson 8-2 p.391

Equations with Two Variables
• In the other chapters, we learned how to solve equations like this:
• 5x + 3 = 2x +9
• In this type of equation, there was only one kind of variable—”x”.
• Now we will learn how to solve variables like: y = 2x + 3
Equations with Two Variables

y = 2x + 3

Equations with Two Variables
• y = 2x + 3
• What do you notice about this equation? Yes there are two kinds of variables—an x and a y.
• We will find in this chapter that the solution to this type of equation is an ordered pair and if we graph the ordered pairs of the equation, we get a straight line when the points are connected.
Equations with Two Variables
• We will also find that an equation like y = 2x + 3 can have many solutions, not just one, but it is the graph of the solutions that will be our answer.
• Let’s start with one way to solve this type of problem. . .a t-table or t-chart
Equations with Two Variables
• y = 2x + 3
• One strategy is to make a table of values or a t-table.
• It looks like this:

X Y

Equations with Two Variables
• y = 2x + 3
• We begin by choosing any value we want for x. This may seem odd to you, but the reason will become apparent later.
• I like to choose one positive number, one negative number and the number zero.
Equations with Two Variables
• y = 2x + 3 Let’s choose 1, 0 and -2

x y

1 Place the x values in

0 the chart. This reminds

-2 us which numbers to

substitute for x.

Equations with Two Variables
• y = 2x + 3 Then we substitute each

value one at a time and

x y solve for “y”

1 52(1) + 3 = 5

0

-2

Equations with Two Variables
• y = 2x + 3 Then we substitute each

value one at a time and

x y solve for “y”

1 52(1) + 3 = 5

0 3 2(0) + 3 = 3

-2

Equations with Two Variables
• y = 2x + 3 Then we substitute each

value one at a time and

x y solve for “y”

1 52(1) + 3 = 5

0 3 2(0) + 3 = 3

-2 -1 2(-2) + 3 = -1

Equations with Two Variables
• The information in the t-table is a series of ordered pairs that when graphed on the coordinate plane, will result in a straight line like this
Equations with Two Variables

x y

1 5

0 3

-2 -1

First, plot point (1,5)

Equations with Two Variables

x y

1 5

0 3

-2 -1

First, plot point (1,5)

Equations with Two Variables

x y

1 5

0 3

-2 -1

First, plot point (1,5)

Then plot point (0,3)

Equations with Two Variables

x y

1 5

0 3

-2 -1

First, plot point (1,5)

Then plot point (0,3)

Equations with Two Variables

x y

1 5

0 3

-2 -1

First, plot point (1,5)

Then plot point (0,3)

Then plot point (-2,-1)

Equations with Two Variables

x y

1 5

0 3

-2 -1

First, plot point (1,5)

Then plot point (0,3)

Then plot point (-2,-1)

Finally draw a line that connects and goes through the points.

Equations with Two Variables

This is the graph of the equation:

y = 2x + 3

We will find that each equation has its own unique graph.

Try This
• Make a t-table for the equation

y = 3x -2 using the following values

for x

x y

3

0

-1

Try This
• Make a t-table for the equation

y = 3x -2 using the following values

for x

x y

3 73(3) – 2 = 7

0

-1

Try This
• Make a t-table for the equation

y = 3x -2 using the following values

for x

x y

3 73(3) – 2 = 7

0 -2 3(0) – 2 = -2

-1

Try This
• Make a t-table for the equation

y = 3x -2 using the following values

for x

x y

3 73(3) – 2 = 7

0 -2 3(0) – 2 = -2

-1 -5 3(-1) – 2 = -5

Try This

x y

3 7

0 -2

-1 -5

Now graph the

Ordered pairs

Try This

x y

3 7

0 -2

-1 -5

One more Thing
• Sometimes, an equation will be given as well as a sample ordered pair, and you will be asked “Is this a solution to the equation?”
• For example, is (4,3) a solution to this equation: y = -2x + 2
• Substitute the ordered pair in the solution: 3 = -2(4) + 2

In this case 3 = -8 + 2 or

3 = -6 is not true, so no it is not a solution.

Try This
• Is (3,0) a solution to y = 2x – 6
• 0 = 6 – 6
• 0=0
• Is (-2,5) a solution to y = -3x + 1
• 5 = 7
Try This
• Is (3,0) a solution to y = 2x – 6 yes
• Is (-2,5) a solution to y = -3x + 1 no
2-3-11 Agenda

PA#13:

Pp.394-395

#12-18 even, 20-30 even