Algebra 1 Semester Study Guide

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 one solution?

Back

It means that the equations represent lines that intersect at exactly one point.

Front

What does it mean if a system of equations has infinite 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 system of equations has no solution?

Back

If simplifying the equations leads to a false statement, such as 0=5, it has no solution.

Front

How do you determine if a system of equations has one solution?

Back

If simplifying the equations leads to a true statement with different slopes, it has one solution.

Front

How do you determine if a system of equations has infinite solutions?

Back

If simplifying the equations leads to a true statement that is always true, such as 0=0, it has infinite solutions.

Front

What is a continuous relationship in mathematics?

Back

A relationship where changes in one variable result in continuous changes in another variable, such as distance over time.

Front

Give an example of a discrete relationship.

Back

The number of cows a farmer owned over the years, as it can only take whole number values.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run (change in y over change in x).