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 any ordered pair that satisfies all inequalities in the system.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane, shading the region that satisfies each inequality.

Front

What does it mean if a point is a solution to a system of inequalities?

Back

If a point is a solution, it lies in the shaded region of the graph for all inequalities in the system.

Front

What is the difference between a solution to an equation and a solution to an inequality?

Back

A solution to an equation is a specific point that makes the equation true, while a solution to an inequality is a range of values that satisfy the inequality.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane, which is the region of the graph that satisfies the inequality.

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

Back

The feasible region is the area on the graph where all the shaded regions of the inequalities overlap, representing all possible solutions.

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How can 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 and check if all inequalities are satisfied.

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What is the significance of the boundary line in a linear inequality?

Back

The boundary line represents the points where the inequality changes from true to false. It is solid for '≤' or '≥' and dashed for '<' or '>'.

Front

What is an example of a system of inequalities?

Back

Example: y > 2x + 1 and y ≤ -x + 4.