3 Variable Systems by Elimination

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 simultaneously.

Front

What does it mean to solve a system of equations by elimination?

Back

Solving by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variables.

Front

What is the elimination method?

Back

The elimination method is a technique for solving systems of equations by removing one variable, allowing for simpler equations to solve.

Front

How do you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines, meaning they never intersect.

Front

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

Back

Infinitely many solutions occur when the equations represent the same line, meaning every point on the line is a solution.

Front

What is the first step in solving a system of equations by elimination?

Back

The first step is to align the equations and manipulate them to create coefficients that can be easily eliminated.

Front

How can you check your solution to a system of equations?

Back

You can check your solution by substituting the values back into the original equations to see if they hold true.

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 do not intersect.

Front

What is the significance of the coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines represented by the equations, affecting their intersection.