systems of equations and inequalities review

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values for the variables that makes all equations true simultaneously.

Front

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

Back

Substitute the point's coordinates into each equation. If all equations are satisfied, the point is a solution.

Front

What does a solid line represent in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, which occurs when the inequality has 'or equal to'.

Front

What does a dashed line represent in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, which occurs when the inequality does not have 'or equal to'.

Front

Write a system of equations for the following scenario: The cost of 5 squash and 2 zucchini is $1.32, and 3 squash and 1 zucchini cost $0.75.

Back

5q + 2z = 1.32 and 3q + 1z = 0.75.

Front

What is the graphical representation of a system of inequalities?

Back

The graphical representation consists of shaded regions that indicate the solution set, bounded by lines representing the inequalities.

Front

How do you identify a feasible region in a system of inequalities?

Back

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

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 all equations are satisfied.

Front

What is the difference between a consistent and inconsistent system of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

What does it mean for a system of equations to be dependent?

Back

A dependent system has infinitely many solutions, as the equations represent the same line.