1 / 8

Find Solutions of equations in two variables.

Find Solutions of equations in two variables. 8.2. Example 1: [Checking a Solution]. x, y. Tell whether (-1, 19) is a solution of 5 x + 6y = 100. Write original equation: 5x + 6y = 100 Substitute -1 for x and 19 for y. 5(-1) + 6(19) 100 Simplify. 109 ≠ 100

jaron
Download Presentation

Find Solutions of equations in two variables.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Find Solutions of equations in two variables. 8.2

  2. Example 1: [Checking a Solution] x, y Tell whether (-1, 19) is a solution of 5x + 6y = 100 Write original equation: 5x + 6y = 100 Substitute -1 for x and 19 for y. 5(-1) + 6(19) 100 Simplify. 109 ≠ 100 Answer: (-1, 19) is not a solution of 5x + 6y = 100

  3. Example 2: Finding Solutions You are saving money for a stereo system. So far, you have $40 saved. For every lawn you mow, you earn $20. Use the equation t = 40 + 20m, where t represents the total amount saved and m is the number of lawns mowe. Make a table of solutions for the equation. How many lawns will you have to mow to save a total of $400? Substitute values of m into the equation t = 40 + 20m, and find the values of t. The table shows that the following ordered pairs are solutions of the equations: (0, 40), (10, 240), (25, 540) Find the value of m when t = 400. 400 = 40 + 20m; Substitute 400 for t in the equation 360 = 20m; Subtract 40 from each side. 18 = m; Divide each side by 20. Answer: You will have to mow 18 lawns to save a total of $400.

  4. You practice: Tell whether the ordered pair is a solution of 2y – 9x = -11 1. (5, 17); 2y – 9x = -11 A solution of an equation in x and y is an ordered pair (x,y) that produces a true statement when the values of x and y are substituted into the equation. 2(17) – 9(5) = -11 34 – 45 -11 -11 = -11; [therefore, (5, 17) is a solution of 2y – 9x = -11] Make a table of solutions for the equation. Then find x when y = 0 3x + y =15 Video: When y = 0 then x is 5. http://www.virtualnerd.com/pre-algebra/algebra-tools/relations-ordered-pairs-coordinate-plane/ordered-pairs-coordinate-plane/test-ordered-pair-equation-solution

  5. http://youtu.be/0gKjSOuLQuw Example 3: Graphing a Linear Equations Write 4y – 12x = 8 in function form. Then graph the equation. Function form is when you solve for y. Solution: To write the equation in function form, solve for y. 4y – 12x = 8 Write original equation Video: 4y = 12x + 8 Add 12x to each side See next slide for graphing ordered pairs. y = 3x + 2 Divide each side by 4 To graph the equation, use its function form to make a table of solutions. Graph the ordered pairs (x, y) from the table, and draw a line through the points.

  6. http://www.teachertube.com/viewVideo.php?video_id=172455 --2

  7. Example4: Graphing Horizontal and Vertical Lines The graph of the equation y = b is the horizontal line through (0,b). An example is Graph y = 3. If you were to graph (0,3) you would create a horizontal graph. To graph a horizontal line all y –coordinates are the same….. ( 0, 3); (1, 3); (-1,3); (3,3) X http://youtu.be/avS6C6_kvXM X Video To graph a vertical line all x-coordinates are the same…… (-2, 0); (-2, 1); (-2, -1) http://www.virtualnerd.com/algebra-1/linear-equation-analysis/intercept/horizontal-vertical-lines/horizontal-line-graph-example http://www.virtualnerd.com/algebra-1/linear-equation-analysis/intercept/horizontal-vertical-lines/vertical-line-graph-example Videos

  8. Practice Problems • Complete the statement: An equation that is solved for y is in __________ form. Tell whether the ordered pair is a solution of the equation. • y = x; (-3, 3) 3. y = 3x + 7; (-2, 1) Tell whether the ordered pair is a solution of y = -3x + 9 • (2,4) 5. (1, 3) 5. (-3, 18) Graph the equation: Hint: Create a table for x and y. • y = x + 4 7. y = -x + 2 Write the equation in function form. Then graph the equation. 8. 4x + 4y = 8 9. 5x – y = -1 10. 2y + 3x = 2

More Related