M2T1 Systems of Inequalities Word Problems

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.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the inequalities overlap.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≤ or ≥) or dashed line (for < or >). 2. Shade the region that satisfies the inequality.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution if it lies within the shaded region of the graph representing the inequalities.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates they are not included (< or >).

Front

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

Back

The feasible region is the area on a graph where all the inequalities in the system are satisfied.

Front

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

Back

Substitute the point's coordinates into each inequality. If all inequalities are true, the point is a solution.

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 the values satisfy all equations simultaneously.

Front

What does it mean to have no solution in a system of equations?

Back

No solution occurs when the lines representing the equations are parallel and never intersect.

Front

What does it mean to have infinitely many solutions in a system of equations?

Back

Infinitely many solutions occur when the equations represent the same line, meaning every point on the line is a solution.