Systems of Equations and Inequalities Quick Check

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

A point is a solution if it satisfies all equations in the system.

Front

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

Back

Substitute the point into each inequality; if it satisfies all, it is a solution.

Front

What is the graphical representation of a system of equations?

Back

The intersection point(s) of the lines representing the equations.

Front

What is an inequality?

Back

A mathematical statement that compares two expressions using <, >, ≤, or ≥.

Front

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

Back

A feasible solution is one that satisfies all constraints of the inequalities.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line; it represents the rate of change.

Front

How do you find the intersection of two lines represented by equations?

Back

Set the equations equal to each other and solve for the variable.

Front

What is the meaning of 'b' in the equation y = mx + b?

Back

'b' is the y-intercept, the point where the line crosses the y-axis.

Front

What does the term 'solution set' refer to?

Back

The collection of all possible solutions to a system of equations or inequalities.