Systems 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 if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

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

Front

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

Back

Substitute the point's coordinates into each equation; if they satisfy all equations, it is a solution.

Front

What is an inequality?

Back

A mathematical statement that compares two expressions, showing that one is greater than, less than, or equal to the other.

Front

What is the difference between '>' and '≥'?

Back

'>' means greater than, while '≥' means greater than or equal to.

Front

How do you graph a linear inequality?

Back

Graph the corresponding equation as a line, then shade the region that satisfies the inequality.

Front

What does the slope of a line represent in a linear equation?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are integers.