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2-3-11

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

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  1. 2-3-11 • Please have hw out to correct.

  2. Equations with Two Variables Lesson 8-2 p.391

  3. 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

  4. Equations with Two Variables y = 2x + 3 • What do you notice about this equation?

  5. 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.

  6. 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

  7. 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

  8. 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.

  9. 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.

  10. 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

  11. 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

  12. 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

  13. 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

  14. Equations with Two Variables x y 1 5 0 3 -2 -1 First, plot point (1,5)

  15. Equations with Two Variables x y 1 5 0 3 -2 -1 First, plot point (1,5)

  16. Equations with Two Variables x y 1 5 0 3 -2 -1 First, plot point (1,5) Then plot point (0,3)

  17. Equations with Two Variables x y 1 5 0 3 -2 -1 First, plot point (1,5) Then plot point (0,3)

  18. 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)

  19. 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.

  20. 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.

  21. Try This • Make a t-table for the equation y = 3x -2 using the following values for x x y 3 0 -1

  22. 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

  23. 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

  24. 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

  25. Try This x y 3 7 0 -2 -1 -5 Now graph the Ordered pairs

  26. Try This x y 3 7 0 -2 -1 -5

  27. 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.

  28. 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

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

  30. 2-3-11 Agenda PA#13: Pp.394-395 #12-18 even, 20-30 even

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