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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”.

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2 3 11

2-3-11

  • Please have hw out to correct.


Equations with two variables

Equations with Two Variables

Lesson 8-2 p.391


Equations with two variables1

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 variables2

Equations with Two Variables

y = 2x + 3

  • What do you notice about this equation?


Equations with two variables3

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 variables4

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 variables5

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 variables6

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 variables7

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 variables8

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 variables9

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 variables10

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 variables11

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 variables12

Equations with Two Variables

x y

1 5

0 3

-2 -1

First, plot point (1,5)


Equations with two variables13

Equations with Two Variables

x y

1 5

0 3

-2 -1

First, plot point (1,5)


Equations with two variables14

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 variables15

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 variables16

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 variables17

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 variables18

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

Try This

  • Make a t-table for the equation

    y = 3x -2 using the following values

    for x

    xy

    3

    0

    -1


Try this1

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 this2

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 this3

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


Try this4

Try This

xy

37

0 -2

-1 -5

Now graph the

Ordered pairs


Try this5

Try This

xy

37

0 -2

-1 -5


One more thing

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 this6

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 this7

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

2-3-11 Agenda

PA#13:

Pp.394-395

#12-18 even, 20-30 even


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