solve each of the following systems of linear inequalities graphically. 3x - y<( little line under arrow) 6,

Question

x >(little line under arrow) 1
y <(little line under arrow) 3

Answer 1

For future reference, the "little line under arrow" you refer to translates to "greater than or equal to", and is best represented by >=. Similarly, less than or equal to is represented by <=.

3x - y <= 6
x > 1
y < 3

Therefore,

3x - y <= 6
1 < x
y < 3

Change the first to slope-intercept form, even if there's no equal sign.

3x - y <= 6
-y <= -3x + 6
At this point i'm going to multiply both sides by -1. This switches the inequality sign.
y >= 3x - 6

So all you have to do is graph y = 3x - 6. You'll either be shading the right side of the line or the left side. To know which one to shade, test a point: (0,0), and see if the inequality holds true.
0 >= 3(0) - 6?
0 >= 0 -6?
0 >= -6? No; therefore you shade the part of the line that DOESN'T contain (0,0.

To shade x > 1, you graph x = 1 (a vertical line), and make it dotted (because it's strictly greater than 1, and not >=). Now, shade everything to the right of it.

To shade y < 3, graph y = 3 (horizontal line), make it a dotted line, and shade everything below it.

The intersection of the shades is how to solve it graphically.