How to Solve & Graph a Solution Set

Solve and graph the solution set for 2x + 3y = 12

• 1

  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

• 2

  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);

• 3

  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)

• 4

  Draw a line connecting all four point. The result will be the graph of the solution set for 2x + 3y = 12