Solving Systems of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations in the system.

Front

What are the three main methods for solving systems of equations?

Back

The three main methods are: 1) Substitution, 2) Elimination, 3) Graphing.

Front

When is substitution the best method to use?

Back

Substitution is best used when one equation is easily solvable for one variable.

Front

What does it mean to eliminate a variable in a system of equations?

Back

To eliminate a variable means to manipulate the equations so that one variable is removed, allowing for the other variable to be solved.

Front

What is the elimination method?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

How do you determine which variable to eliminate?

Back

Choose the variable that can be easily eliminated, often based on the coefficients of the variables in the equations.

Front

What is the graphical interpretation of a system of equations?

Back

The graphical interpretation involves plotting the equations on a coordinate plane; the solution is the point(s) where the graphs intersect.

Front

What does it mean if two equations in a system have the same slope but different y-intercepts?

Back

If two equations have the same slope but different y-intercepts, they are parallel lines and have no solution.

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.