Find Solutions of equations in two variables.

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