One big difference between systems of equations and systems of inequalities is how they work and the challenges they can create.

1. Definitions:

   • A system of equations is when you have two or more equations. These equations show how different variables are related. The main goal is to find the exact values for those variables that make all the equations true at the same time.
   • A system of inequalities uses inequalities like $>$, $<$, $\geq$, or $\leq$. This makes things a little trickier because instead of just one answer, the solution is a range of values that meet several conditions.

2. Graphical Representation:

   • When you graph systems of equations, they look like lines (or planes if you think in three dimensions). The solution is where these lines meet, which is usually just one point.
   • On the other hand, systems of inequalities create a shaded area on the graph. This shaded area shows all the possible solutions that fit the given conditions. Sometimes, figuring out where the boundaries are can be confusing.

3. Solutions:

   • To find a solution for systems of equations, you can use methods like substitution or elimination. This often leads to a clear answer.
   • However, solving systems of inequalities is a bit more complex. You need to analyze where the shaded areas overlap and check different parts of the graph.

These challenges may seem tough at first, but you can get better with practice! By using graphing methods and algebra techniques step-by-step, you can really improve your understanding of systems of equations and inequalities.