Question 122041: Solve each of the following systems of linear inequalities graphically.
3x-y ≤ 6
x ≥1
y ≤ 3
I would truly appreciate it if someone could help me out with this. I believe I may be making it harder than it is and I have completely confused myself. Thank you so much for taking the time to help!!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Here's the quick and easy way to graph inequalities.
First, pretend it is an equation, and graph the line that would be represented by that equation. When you draw the line on the graph, look at the original inequality to see if "or equal" is included as it is in your three examples. If it is, make the line a solid line. If not, make the line a dashed line.
Next pick a convenient point on either side of, but not on the line. For example, your first problem is a line with a slope of 3 that intercepts the y-axis at -6. Pick a point above and to the left of the line; (1,1) is a convenient choice.
Now substitute the x- and y-coordinates from the chosen point into the original inequality.
 .
Since 2 is, in fact, less than 6, you have chosen a point on the 'correct' side of the line. Shade in the entire plane on this side of the line. If, on the other hand, you had chosen a point that made the inequality a false statement, you will know that you have chosen a point on the wrong side of the line, so shade in the other side.
Hint for problem 2:  is a vertical line that crosses the x-axis at (1,0).
Hint for problem 3:  is a horizontal line that crosses the y-axis at (0,3).
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