Algebra I A Chapter 6

Front

What is a system of equations?

Back

A set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the substitution method in solving equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is a zero pair in the context of equations?

Back

A pair of numbers that add up to zero, used to eliminate a variable when solving systems of equations.

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and intercepts of the lines represented by the equations.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines on a graph represent the solutions to the system.

Front

What is the first step in using the substitution method?

Back

Solve one of the equations for one variable in terms of the other variable.

Front

What is the importance of checking your solution in a system of equations?

Back

To ensure that the values found satisfy all equations in the system.