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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”.

2-3-11

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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

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:

XY

### 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

xy

1Place the x values in

0the chart. This reminds

-2us which numbers to

substitute for x.

### Equations with Two Variables

• y = 2x + 3Then we substitute each

value one at a time and

x ysolve for “y”

1 52(1) + 3 = 5

0

-2

### Equations with Two Variables

• y = 2x + 3Then we substitute each

value one at a time and

x ysolve for “y”

1 52(1) + 3 = 5

0 32(0) + 3 = 3

-2

### Equations with Two Variables

• y = 2x + 3Then we substitute each

value one at a time and

x ysolve for “y”

1 52(1) + 3 = 5

0 32(0) + 3 = 3

-2 -12(-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

xy

3

0

-1

### Try This

• Make a t-table for the equation

y = 3x -2 using the following values

for x

xy

373(3) – 2 = 7

0

-1

### Try This

• Make a t-table for the equation

y = 3x -2 using the following values

for x

xy

373(3) – 2 = 7

0 -23(0) – 2 = -2

-1

### Try This

• Make a t-table for the equation

y = 3x -2 using the following values

for x

xy

373(3) – 2 = 7

0 -23(0) – 2 = -2

-1 -53(-1) – 2 = -5

xy

37

0 -2

-1 -5

Now graph the

Ordered pairs

xy

37

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