2.3 and 2.4 System of Equation

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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What is a solution to a system of inequalities?

Back

A solution to a system of inequalities is a set of values that satisfy all inequalities in the system, often represented as a region on a graph.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does it mean for a point to be 'not a solution' to a system of inequalities?

Back

A point is 'not a solution' if it does not satisfy at least one of the inequalities in the system.

Front

What is the graphical representation of a system of inequalities?

Back

The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of the inequalities.

Front

What is the difference between a system of equations and a system of inequalities?

Back

A system of equations has exact solutions (points of intersection), while a system of inequalities has a range of solutions (regions) that satisfy the inequalities.

Front

What is the first step in solving a system of inequalities by graphing?

Back

The first step is to graph each inequality on the same coordinate plane, using dashed lines for '<' or '>' and solid lines for '≤' or '≥'.

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What does the term 'feasible region' refer to in the context of inequalities?

Back

The feasible region is the area on a graph where all the inequalities overlap, representing all possible solutions to the system.

Front

How can you check if a point lies within the feasible region?

Back

Substitute the point's coordinates into each inequality. If it satisfies all inequalities, it lies within the feasible region.

Front

What is the significance of the intersection point in a system of equations?

Back

The intersection point represents the solution to the system, where both equations are satisfied simultaneously.