Algebra 1 Item No 59

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Algebra 1 Item No 59

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

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