5. What does solving a system of equations or inequalities mean? What are you finding?

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Solving a system of equations or inequalities involves finding the values of the variables that satisfy all the equations or inequalities in the system simultaneously. Here's a breakdown of what this means:

1. **System of Equations**: A system of equations consists of two or more equations that share the same set of variables. The solution to the system is the set of values for the variables that make all the equations true at the same time.

- **Example**: Consider the system:
     $$
     \begin{align*}
     2x + 3y &= 6 \
     x - y &= 1
     \end{align*}
     $$
     The solution would be the values of $$x$$ and $$y$$ that satisfy both equations.

2. **System of Inequalities**: A system of inequalities consists of two or more inequalities that involve the same variables. The solution is the set of values that satisfy all the inequalities simultaneously.

- **Example**: Consider the system:
     $$
     \begin{align*}
     x + y &> 2 \
     x - y &\leq 3
     \end{align*}
     $$
     The solution would be the region in the coordinate plane where both inequalities hold true.

### What Are You Finding?

When you solve a system of equations or inequalities, you are essentially finding:

- **Intersection Points**: For equations, you are finding the points where the graphs of the equations intersect. This point (or points) represents the values of the variables that satisfy all equations in the system.

- **Feasible Region**: For inequalities, you are identifying a region in the coordinate space that satisfies all the inequalities. This region represents all possible solutions that meet the conditions set by the inequalities.

In summary, solving a system of equations or inequalities means determining the values of the variables that make all the equations or inequalities true, which can be visualized as finding points of intersection or regions in a graph.
Solving a system of equations or inequalities means finding the values of the variables that satisfy all the equations or inequalities at the same time.

5. What does solving a system of equations or inequalities mean? What are you finding?

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