A solution set for an equation where y = f (x) is a set of (x, y) values that make the equation true. For example, for the equation y = 2x, a solution set will be the (x, y) values (1, 2) and (2, 4) because, when x is 1, y is 2 and when x is 2, y is 4. When you have two or more (x, y) points in the solution set, you can graph the solution set.
Solve the equation to get y in terms of x:
Subtract 2x from both sides:
2x + 3y - 2x = 12 - 2x 3y = 12-2x
Divide both sides by 3 to get y on the leftside by itself:
3y/3 = (12-2x)/3
y = (12-2x)/3
Calculate a solution set. As an example, calculate the solution set for x = 1, 2, 3 and 4:
x = 1 y = (12- (2)(1))/3 = 10/3 = 3.33; Solution set point: (1, 3.33)
x = 2 y = (12- (2)(2))/3 = 8/3 = 2.66 Solution set point: (2, 2.66);
x = 3 y = (12- (2)(3))/3 = 6/3 = 2. Solution set point: (3, 2);
x = 4 y = (12- (2)(4))/3 = 4/3 = 1.33. Solution set point: (4, 1.33);
Graph the solution set. Draw an x-y graph. Place 5 hash marks on both the x and y axis and label the hash marks 1 through 5. Start by plotting the point (1, 3.33). Go to the x-axis where x = 1. While on x= 1, go up vertically on the y axis to the point 3.33, between the 3 and 4 hash marks, and place a dot at that point. Next plot the point (2, 2.66). Go to the x-axis where x = 2. While on x = 2, go up vertically to the point 2.66, between the 2 and 3 hash marks, and place a dot at that point. Repeat this process for points (3, 2), (4, 1.33)
Draw a line connecting all four point. The result will be the graph of the solution set for 2x + 3y = 12
