A graph of the system of inequalities is shown on the coordinate plane in the image attached below.
A possible solution is (4, -4).
In Mathematics, there are several rules that are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a graph and these include the following:
- The line on a graph should be a dashed line when the inequality symbol is (> or <).
- The inequality symbol should be less than (<) when a dashed line is shaded below.
- The inequality symbol should be greater than or equal to (≥) when a solid line is shaded above.
In this context, we can logically deduce that the graph of this linear inequality, 5x+7y≤-5 would be a solid line and shaded below while the graph of this linear inequality, 3x+2y>2 would be a dashed line and shaded above. The solution area is the region shaded green to the left on the graph and a possible solution is (4, -4).
Complete Question:
3x+2y>2
5x+7y≤-5
Graph both lines and the solution to the system of linear inequalities.