Entrance Exam - Systems (LT #15 & 16)

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 graphs of the inequalities overlap.

Front

What does it mean if a system of linear equations has infinitely many solutions?

Back

It means that the equations represent the same line, and any point on that line is a solution to the system.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

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

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the graphical representation of a linear inequality?

Back

A linear inequality is represented by a shaded region on one side of the line, indicating all the solutions that satisfy the inequality.

Front

What does the symbol '>' indicate in an inequality?

Back

The symbol '>' indicates that the value on the left is greater than the value on the right.

Front

What does the symbol '<' indicate in an inequality?

Back

The symbol '<' indicates that the value on the left is less than the value on the right.

Front

What is the significance of the boundary line in a system of inequalities?

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

How can you tell if a system of inequalities is consistent?

Back

A system of inequalities is consistent if there is at least one solution that satisfies all inequalities.

Front

What is a feasible region in the context of linear programming?

Back

The feasible region is the area on a graph that satisfies all constraints of a linear programming problem, representing all possible solutions.