I desperately need guidance. Not only do I not know how to graph these systems of linear inequalities, but I also do not understand the concept whatsoever. I have watched several videos regarding the subject, but I didn't retain anything from them. Please, I desperately need your help.
Graph each system of linear inequalities. Give two ordered pairs that are solutions and two that are not.
1. y < 2x - 1
y > 2
2. x < 3
y > x - 2
3. y => 3x
3x + y => 3
4. 2x - 4y <= 8
y > x - 2
I don't know if your name is Victoria, but here is her post with the same question as yours.
I think my answer applies well here
http://www.jiskha.com/display.cgi?id=1389322523
I understand that graphing systems of linear inequalities can be a challenging concept at first, but I'm here to help! Let's break it down step by step.
To graph a linear inequality, we first need to understand what the inequality represents in terms of a line on a graph.
1. y < 2x - 1
y > 2
Let's start with the first inequality, y < 2x - 1. We can draw the line y = 2x - 1, but since it is less than (<), we need to draw a dashed line instead of a solid line to represent that it is not included in the solution. This line represents all the points on the line itself.
Next, the inequality y > 2 represents a horizontal line at y = 2. Since it is greater than (>), again we draw a dashed line to represent that it is not included.
Now, let's shade the region that satisfies both inequalities. Since we have y < 2x - 1 and y > 2, we want to shade the area between the lines where y is less than 2x - 1 and greater than 2.
To test for solutions, you can choose any ordered pairs within the shaded region. For example, (0,0) and (1,3) are solutions that satisfy both inequalities. Conversely, (-1,1) and (2,1) are two ordered pairs that do not satisfy the inequalities.
2. x < 3
y > x - 2
For the second system of inequalities, we start with x < 3 which represents a vertical line at x = 3. Since it is less than (<), we draw a dashed line to represent it.
Next, y > x - 2 represents a line with a slope of 1 and y-intercept of -2. Again, draw a dashed line since it is greater than (>).
Now, shade the region that satisfies both inequalities which lies to the left of the vertical line x = 3 and above the line y = x - 2.
Choose ordered pairs within the shaded region to test for solutions. For example, (1,3) and (2,4) are solutions that satisfy both inequalities. Conversely, (4,1) and (3,0) are two ordered pairs that do not satisfy the inequalities.
3. y >= 3x
3x + y >= 3
In the third system, y >= 3x represents a line with a slope of 3. Draw a solid line because it is greater than or equal to (>=).
Next, 3x + y >= 3 represents a line with a slope of -3 and y-intercept of 3. Again, draw a solid line because it is greater than or equal to (>=).
Shade the region that satisfies both inequalities which lies above the line y = 3x and above or on the line 3x + y = 3.
To test for solutions, choose ordered pairs within the shaded region. For example, (1,3) and (0,3) are solutions that satisfy both inequalities. On the other hand, (-1,-2) and (2,0) are examples of ordered pairs that do not satisfy the inequalities.
4. 2x - 4y <= 8
y > x - 2
In the fourth system, we start with the inequality 2x - 4y <= 8. Rewrite it as y >= (1/2)x - 2 to obtain the equation of the line.
Next, y > x - 2 represents a line with a slope of 1 and a y-intercept of -2.
Now, shade the region that satisfies both inequalities. For this system, shade the region below the line 2x - 4y = 8 and above the line y = x - 2.
To test for solutions, choose ordered pairs within the shaded region. For example, (0,0) and (1,-1) are solutions that satisfy both inequalities. However, (2,0) and (-1,2) are not solutions to the system.
I hope this explanation helps you understand how to graph systems of linear inequalities. Remember to plot the lines, shade the regions that satisfy both inequalities, and test ordered pairs to confirm solutions!