Steve S. answered • 03/15/14
Tutor
5
(3)
Tutoring in Precalculus, Trig, and Differential Calculus
4x + 10y < 40
-6x - 8y < 48
Every line creates 3 sets of points on a Cartesian Plane: 1) the points on the line, 2) the points in the plane on one side of the line, and 3) the points in the plane on the other side of the line.
If an inequality has = in its symbol in addition to < or >, then the points on the line are included; otherwise they’re not.
4x + 10y < 40 is just all the points in a half plane on one side of the line 4x + 10y = 40. We draw the line with dashes to indicate the points on it are not in the solution set for the inequality. Then we test a point to see if it satisfies the inequality; if so, shade the half plane on the side of the line that includes the point, otherwise shade the half plane on the other side. In this case, (0,0) satisfies the inequality so we would shade the half plane that included (0,0).
The line -6x - 8y < 48 will be drawn dashed, and the point (0,0) is in the solution set so the half plane that includes (0,0) will be shaded.
The solution to the system of inequalities is the overlap of the two shaded regions; i.e., the points that are in the solution sets of both inequalities.
To draw the two lines just find the intercept points (a,0) and (0,b) for each and draw the line through them.
4x + 10y < 40 => (0,4), (10,0)
-6x - 8y < 48 => (0,-6), (-8,0)
After you’ve sketched your solution, check out: http://www.wyzant.com/resources/files/265291/system_of_inequalities
-6x - 8y < 48
Every line creates 3 sets of points on a Cartesian Plane: 1) the points on the line, 2) the points in the plane on one side of the line, and 3) the points in the plane on the other side of the line.
If an inequality has = in its symbol in addition to < or >, then the points on the line are included; otherwise they’re not.
4x + 10y < 40 is just all the points in a half plane on one side of the line 4x + 10y = 40. We draw the line with dashes to indicate the points on it are not in the solution set for the inequality. Then we test a point to see if it satisfies the inequality; if so, shade the half plane on the side of the line that includes the point, otherwise shade the half plane on the other side. In this case, (0,0) satisfies the inequality so we would shade the half plane that included (0,0).
The line -6x - 8y < 48 will be drawn dashed, and the point (0,0) is in the solution set so the half plane that includes (0,0) will be shaded.
The solution to the system of inequalities is the overlap of the two shaded regions; i.e., the points that are in the solution sets of both inequalities.
To draw the two lines just find the intercept points (a,0) and (0,b) for each and draw the line through them.
4x + 10y < 40 => (0,4), (10,0)
-6x - 8y < 48 => (0,-6), (-8,0)
After you’ve sketched your solution, check out: http://www.wyzant.com/resources/files/265291/system_of_inequalities