Graphing Systems of Inequalities and Equations

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 if two lines are parallel in a system of equations?

Back

It means there is no solution to the system because the lines never intersect.

Front

What is the graphical representation of a solution to a system of inequalities?

Back

The solution is represented by the shaded region where the inequalities overlap on a graph.

Front

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

Back

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

Front

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

Back

It means the equations represent the same line, and every point on the line is a solution.

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 y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x=0.

Front

How can you tell if a system of equations has one solution?

Back

If the lines intersect at exactly one point, the system has one solution.

Front

What is the difference between a solution to an equation and a solution to an inequality?

Back

A solution to an equation is a specific point, while a solution to an inequality is a range of values.

Front

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

Back

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