Question

Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y < 2x - 5 y ≤ -x - 2

Answer 1

First, we need to graph the lines:

`\begin{gathered} y=2x-5\text{ (slope = 2 and y-intercept = -5)} \\ y=-x-2\text{ (slope = -1 and y-intercept = -2)} \end{gathered}`

In the solution of the first inequality, the points on the line are not included, then this line must be dashed. On the other hand, in the solution of the second inequality, the points on the line are included, then this line must be solid.

In both cases, the solution to each inequality is the area below each line.

Combining this information we get the next graph:

where the solution is the orange area.

From the above graph, one point in the solution set is (1, -7). We can check if this point is part of the solution by replacing it into the inequalities, as follows:

`\begin{gathered} -7<2(1)-5 \\ -7<-3\text{ (True)} \\ \text{And} \\ -7\le-1-2 \\ -7\le-3\text{ (True)} \end{gathered}`

Given that the point satisfies both inequalities, then it is part of the solution set.