Solve each of the following systems of linear inequalities graphically. 3x – y 6?

Question

Solve each of the following systems of linear inequalities graphically.
3x – y 6

Can you please include all steps to this problem so i know how to do it.

Answer 1

You left out the inequality sign, but the method for all possibilities is essentially the same.

Start by solving the inequality for y. For example, if your problem is 3x - y ≤ 6,

3x - y ≤ 6
3x ≤ 6 + y
3x - 6 ≤ y
or equivalently,
y ≥ 3x - 6

Now, replace the inequality sign by an equals sign:

y = 3x - 6

This is the equation of a line, of slope 3 and with y-intercept of -6, which forms the boundary of the solution region. Graph this line lightly; if the inequality is ≤ or ≥, make the graph of the line solid; if the inequality is < or >, make the graph of the line dotted.

Finally, if the inequality is < or ≤, the solution region is that part of the xy-plane below the line you've drawn; if the inequality is > or ≥, the solution region is that part of the xy-plane above the line you've drawn.