Solving Systems of Equations Using Substitution or 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?

Back

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

Front

What is the substitution method?

Back

A method for solving a system of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method?

Back

A method for solving a system 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 values back into the original equations to verify if they hold true.

Front

What is an independent system of equations?

Back

A system that has exactly one solution.

Front

What is a dependent system of equations?

Back

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

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What is an inconsistent system of equations?

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A system that has no solution, where the equations represent parallel lines.

Front

Solve the system: 3x + 2y = 8 and -x + y = -11.

Back

(6, -5)

Front

Solve the system: y = -2x + 5 and y = 2x - 11.

Back

(4, -3)