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 infinite solutions?

Back

It means that the equations represent the same line, and there are countless points that satisfy both equations.

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 is a linear equation?

Back

An equation that makes a straight line when graphed, typically in the form y = mx + b.

Front

What is the slope-intercept form of a linear equation?

Back

The form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you solve for x in the equation 3x + 4 = x + 2(x + 2)?

Back

Combine like terms to get 3x + 4 = x + 2x + 4, which simplifies to 3x + 4 = 3x + 4, indicating infinitely many 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

What is the definition of a variable in algebra?

Back

A symbol, often a letter, that represents an unknown value in mathematical expressions or equations.

Front

What does it mean to isolate a variable?

Back

To manipulate an equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is the purpose of graphing a system of equations?

Back

To visually determine the number of solutions by finding the points of intersection of the lines.