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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 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:

X Y

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

x y

1 Place the x values in

0 the chart. This reminds

-2 us which numbers to

substitute for x.

equations with two variables8
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 variables9
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 variables10
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 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

x y

3

0

-1

try this1
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 this2
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 this3
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 this4
Try This

x y

3 7

0 -2

-1 -5

Now graph the

Ordered pairs

try this5
Try This

x y

3 7

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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