Unit 2: Linear Equations, Inequalities, and Systems Review

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

A system of equations is consistent if there is at least one solution that satisfies all equations in the system.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.

Front

How do you determine the slope of a line from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

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, representing the value of y when x is 0.

Front

What does it mean for an inequality to have a solid line when graphed?

Back

A solid line indicates that the points on the line are included in the solution set, which occurs when the inequality symbol includes 'equal to' (≥ or ≤).

Front

What is the graphical representation of the inequality y > 2x - 4?

Back

The graph will have a dashed line for y = 2x - 4, and the area above the line will be shaded to represent all points where y is greater than 2x - 4.

Front

How can you tell if a system of inequalities has no solution?

Back

A system of inequalities has no solution if the graphs of the inequalities do not overlap, meaning there are no points that satisfy all inequalities.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What does the term 'solution' mean in the context of a system of equations?

Back

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