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Algebra 1 Item No 59
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Algebra 1 Item No 59

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  • 1. Algebra 1 Item No. 59
    • Find the intersection of lines
    • x – y = 1 and 2x – y = 5.
    • A. (-1, -2)
    • B. (0, -1)
    • C. (0, 1)
    • D. (4, 3)
    www.upcatreview.com
  • 2.
    • The intersection of two lines is a point which is a solution to the two equations.
    x + y = 3 2x – y = 3 (2, 1) www.upcatreview.com
  • 3.
    • The intersection of two lines is a point which is a solution to the two equations.
    x + y = 3 2x – y = 3 (2, 1) That means that we can use the coordinates of the point of intersection as x and y values for both equations 2 + 1 = 3 3 = 3 2(2) – 1 = 3 3 = 3 www.upcatreview.com
  • 4.
    • To obtain the intersection of the two lines, we can use any of the following methods:
    • Graphing
    • Substitution
    • Elimination
    www.upcatreview.com
  • 5.
    • To obtain the intersection of the two lines, we can use any of the following methods:
    • Graphing
    • Substitution
    • Elimination
    The crudest of all the methods… thus it’s not advisable to use this one. The easiest to remember www.upcatreview.com
  • 6.
    • To obtain the intersection of the two lines, we can use any of the following methods:
    • Graphing
    • Substitution
    • Elimination
    The crudest of all the methods… thus it’s not advisable to use this one. The easiest to remember We’ll use this one to solve the problem www.upcatreview.com
  • 7.
    • In elimination, as the name implies, we eliminate one of the variables.
    x – y = 1 2x – y = 5 We can try to eliminate y for this problem www.upcatreview.com
  • 8.
    • In elimination, as the name implies, we eliminate one of the variables.
    x – y = 1 2x – y = 5 result: an equation with only one variable We can try to eliminate y for this problem Elimination is done by adding or subtracting the two equations www.upcatreview.com
  • 9.
    • To eliminate y and have only x in our final equation, let’s subtract the two equations
    x – y = 1 2x – y = 5 – – x = – 4 x = 4 www.upcatreview.com
  • 10.
    • Now, we will use the value of x which we got from the previous solution…
    x = 4 www.upcatreview.com
  • 11.
    • Now, we will use the value of x which we got from the previous solution…
    • … and substitute it to any of the given equation and solve for the unknown.
    x = 4 x – y = 1 We will use the first given equation because it’s a lot simpler www.upcatreview.com
  • 12.
    • Now, we will use the value of x which we got from the previous solution…
    • … and substitute it to any of the given equation and solve for the unknown.
    x = 4 x – y = 1 4 – y = 1 – y = 1 – 4 y = 3 We will use the first given equation because it’s a lot simpler www.upcatreview.com
  • 13.
    • The intersection of the two lines is the point with the following values:
    • Thus, the coordinates of the point of intersection is (4, 3).
    x = 4 y = 3 www.upcatreview.com
  • 14.
    • The answer is:
    • D. (4, 3)
    www.upcatreview.com
  • 15. Algebra 1 Item No. 59
    • Find the intersection of lines
    • x – y = 1 and 2x – y = 5.
    • A. (-1, -2)
    • B. (0, -1)
    • C. (0, 1)
    • D. (4, 3)
    www.upcatreview.com