24-25 - Reflashcard Graphing System of Equations and Inequalities

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 system of equations to have a unique solution?

Back

It means the lines represented by the equations intersect at exactly one point.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

It means the lines represented by the equations are the same line, overlapping completely.

Front

How do you graph a linear equation?

Back

You can graph a linear equation by finding two or more points that satisfy the equation and connecting them with a straight line.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The slope indicates the steepness of the line and the direction it goes (positive or negative).

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Front

How do you represent a system of inequalities graphically?

Back

You graph each inequality on the same coordinate plane and find the region where the solutions overlap.

Front

What is the feasible region in a system of inequalities?

Back

The feasible region is the area on the graph that satisfies all the inequalities in the system.