Question

How do you graph the system of inequalities `Y ≥ - 5`, `Y ≤ 2x + 5`, `Y ≤ -2x + 5`?

Answer 1

Please see below.

Explanation:

For drawing the graph of a linear inequality, one needs to first draw the graph of the equation (i.e. with 'equal(=)' sign), which is a straight line.

Now this line divides the Cartesian Plane in three parts - (a) the line itself, on which every point satisfies the equality; (b) this line divides plane in two parts, and in one of them the function will satisfy 'greater than' condition and in the other, it will satisfy 'less than' condition.

For graphing, one may shade the required region. The line in such cases may be shown as 'dotted' indicating points on the line are 'not included'.

For condition 'greater than or equal to', it will be the line along with the region in which it is 'greater than' and in such cases line is shown as 'thick line' and the region representing 'greater than' will be shaded. The line is drawn as thick to indicate that points on the line are included in solution set.

For example, in `Y>=-5`, the straight line `Y=-5` is one parallel to `x` axis but below it and graph of `Y>=-5` will appear as follows. Note that the line is not dotted as equality sign is there and hence points on the line are also included in the solution.

Similarly draw graphs of `Y<=2x+5` and `Y<=-2x+5`. These both have line graphs with `y` intercept as `5` but while first is positively sloping (slope `-2`), second is negatively sloping (slope `-2`). As the inequality is 'less than or equal to', area shaded is 'below' the line, which satisfies the condition. Here too, the line is not dotted as equality sign is there and points on the line are included in the solution.

The graphs should appear as follows: