Chapter 7 math copy

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by Josephine Roberts1 view·Updated Mar 13, 2021
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  1. Hello, My name is Joe Zee, and today I'm going
  2. to teach you about the three ways of solving systems
  3. as well as the three different types of solutions for
  4. system. So let's just jump into it.
  5. The first way to solve the system is graphing, and
  6. that is what.
  7. And the way to do that is you take the
  8. two equations in your systems and you graph those lines
  9. and the point where those two lines meet, which is
  10. I've pointed.
  11. I've kind of pointed it out on the little picture
  12. there. That is the solution.
  13. So let's try an example.
  14. Yeah, here we have the system three X plus two
  15. y equals 12 and two x six x I minus
  16. four y equals 12, and each block on the graph
  17. is, too.
  18. It's a little hard to secret small, but and the
  19. point where those two lines meet is the access three
  20. and the Y is 1.5.
  21. Let's try the next system a solution way to solve
  22. systems. Okay, so the next way to solve a system
  23. is by substitution, which is this one.
  24. So first you substitute for the given coordinates like it
  25. will say y equals or X equals, And then the
  26. other coordinate plus something.
  27. And you will just put what y you're X equals
  28. into, um, the like, two x or two y of
  29. the first equation.
  30. You are substituted it, and then you use the distributive
  31. property to figure out what uh, that is, Then you
  32. will solve the problem.
  33. Algebraic Lee.
  34. And then once you know what And once you have
  35. one of the answers to x y you and put
  36. it into the one of the equations and then you
  37. will solve the equation and basically and then you will
  38. have both answers.
  39. Let's try an example.
  40. And here we have the example I'm going to with
  41. my clicker.
  42. But you can't say that I'm gonna use my finger.
  43. Um, here we have the example of four X plus
  44. two y equals 20 and then beneath that we have
  45. the thing that you are substituted for, which is we
  46. have the given coordinate, which is why equals five X
  47. minus two.
  48. So we put but y equals into why into the
  49. equation. So we have four x plus two five x
  50. minus four equals 20 and if we use the distributive
  51. property. We can turn that into for X plus 10
  52. X minus eight equals 20.
  53. Now, I can simplify that into 14 x fine.
  54. Eight. By combining like terms.
  55. And now we want to get rid of that, The
  56. eight on that one side.
  57. And so we're going to plus eight to both sides.
  58. And so we'll have 14 x equals 28.
  59. And now, if we divide each side of the equation
  60. by 14, we won't get X equals two.
  61. So now we know what X is.
  62. Let's go to the next one.
  63. Okay? And he was the second part of that example.
  64. And so now we know what that X equals two.
  65. So we have four.
  66. Uh huh.
  67. And so it was four X.
  68. And now it is for two, Who plus two y
  69. equals 20.
  70. And so we can, uh, multiplies that.
  71. And then we have eight equal eight plus to y
  72. equals 20.
  73. So if we ah uh huh.
  74. Minus eight from both sides, we will have to y
  75. equals 12.
  76. And then once we we divide both sides by two
  77. so we can isolate why we'll have y equals two.
  78. And so answer it is.
  79. It is X is to y equals sex.
  80. So let next.
  81. Let's try the next way to solve it.
  82. The third way to solve a system is by culmination.
  83. So what to go down?
  84. So, um, if there are two ops, it's in a
  85. system like four X and negative four X.
  86. This is the method you would use.
  87. You arrows subtract the system so they both eat.
  88. So both of the opposites are zero because then you
  89. only have the other one.
  90. Then you solve the remaining problem.
  91. Algebraic Bri So and then, since you have one of
  92. the solutions you like part of the solution you input
  93. into the other equation into or just one of the
  94. equations and then you solve their own alphabetically too, so
  95. you can know what those is.
  96. So let's try the example.
  97. So here we have the equation.
  98. Um, seven X minus four y equals 16 and four
  99. X minus four.
  100. Y equals 32.
  101. So, uh, here we have the both equations, we're adding
  102. them together.
  103. And so, uh, seven x plus five X equals 12
  104. x and four y.
  105. So it's negative for why?
  106. Because, you know, I and then 16 plus 32 equals
  107. 48. And if we can simplify that down to, um
  108. by taking out the zeal, because it's nothing.
  109. So we have 12 x equals 48.
  110. We divide both those style.
  111. It's by 12 to isolate the X, and we have
  112. X equals four.
  113. Let's go on to the second poet of the example.
  114. So now we know that X equals four.
  115. So we have, um instead of five x, we have
  116. 54 plus for y equals 32.
  117. So we so we multiply that and we have 20
  118. plus four y equals 32 and then we minus and
  119. to you from both sides.
  120. So we have for why equals 12.
  121. And then we divide both sides by forward to isolate
  122. why and then we have y equals three.
  123. And so we have it from here.
  124. So we have.
  125. Yeah, And so now we have the X equals four.
  126. So first part of that is four, and the y
  127. equals to the Saudi answer to the solution to that
  128. system is for comma X.
  129. That's the point.
  130. And now let's talk about the three different types of
  131. solutions, So oh, you have the three different types of
  132. solutions. The one solution, which is the one that we
  133. have been finding is when they're both different lines.
  134. Mm. And they only pap us through each other once.
  135. So the only point there was only one place where
  136. they intersect.
  137. So they only have one solution, and then we have
  138. no solutions.
  139. That is when the lines never never touch because they
  140. are paler and because they will never touch.
  141. They have no solutions.
  142. And then we have infinite solutions.
  143. That is when both lines overlap.
  144. And so they yeah, overlapping for just for until the
  145. line ends, which it doesn't.
  146. So just they have infinite solutions.
  147. So thank you.
  148. That has been how to find solutions.
  149. Two systems and the different types of solutions to systems.
  150. Thank you.
  151. And have a nice day.