Systems of Equations and Inequalities Review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for a system of equations to have a unique solution?

Back

It means the graphs of the equations intersect at exactly one point.

Front

What are the possible outcomes for a system of linear equations?

Back

1. One solution (intersecting lines) 2. No solution (parallel lines) 3. Infinitely many solutions (coincident lines)

Front

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

Back

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

Front

What is the graphical representation of a linear inequality?

Back

A region of the coordinate plane that is bounded by a line, with one side shaded to indicate the solutions.

Front

What does the symbol '≤' indicate in an inequality?

Back

It indicates that the value can be less than or equal to the number.

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

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

Back

By solving the equations simultaneously, either through substitution or elimination methods.

Front

What does it mean if two lines are parallel?

Back

They have the same slope but different y-intercepts, and they do not intersect.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.