Final answer:
Both systems of linear inequalities and linear equations involve two-dimensional graphs with straight lines, and are represented with equations in the form y = mx + b.
The main difference is that linear equations have solutions that are exact points on a line, while linear inequalities have solutions that encompass areas within a region.
Step-by-step explanation:
A system of two linear inequalities in two variables and a system of two linear equations in two variables are similar in that both involve finding values that satisfy two conditions in a two-dimensional coordinate system, where one axis corresponds to the independent variable (x) and the other corresponds to the dependent variable (y).
The graph of a linear equation is a straight line, while the graph of a linear inequality is a shaded region. Both systems can be represented in the form y = mx + b, reflecting a linear relationship between x and y.
The difference between the two systems lies in the solutions they represent. Linear equations have solutions that lie exactly on their lines, whereas the solutions for linear inequalities lie within a region bounded by the lines.
When solving a system of linear equations, you find specific point(s) of intersection, while solving a system of inequalities involves finding a range of solutions that satisfy all inequalities simultaneously.
Therefore, the graph of a system of equations results in a point (or possibly lines if they are the same or parallel), whereas the graph of a system of inequalities results in a region.