What makes a system of inequalities different from a system of equations?
A system of inequalities and a system of equations differ in the type of mathematical relationship they represent.
A system of equations consists of two or more equations that are solved simultaneously to find the values of variables that satisfy all the equations. The solution to a system of equations is typically a set of values that satisfies all equations at once. In simple terms, the solution is the point (or points) where the different lines or curves intersect.
On the other hand, a system of inequalities consists of two or more inequalities that need to be satisfied simultaneously. The solution to a system of inequalities is usually a set of values that satisfies all the inequalities. In simple terms, the solution is a region that satisfies all the given inequalities. Instead of individual points of intersection, the solution is an area or a range of values that satisfies all inequalities simultaneously. This can often be represented graphically as shaded regions on a graph.
In summary, a system of equations relates to finding points of intersection for lines or curves, whereas a system of inequalities deals with finding a region of values that satisfy all the inequalities.