Systems of Equations by Substitution and Elimination

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 to solve a system of equations by substitution?

Back

To solve for one variable in terms of the other and then substitute that expression into another equation.

Front

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

Back

To add or subtract equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is the substitution method?

Back

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

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

How do you check the solution of a system of equations?

Back

Substitute the solution back into the original equations to verify that both equations are satisfied.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.

Front

What is a dependent system of equations?

Back

A system that has infinitely many solutions, where the equations represent the same line.

Front

How do you represent a system of equations graphically?

Back

By plotting each equation on the same coordinate plane and finding the point(s) where they intersect.