Systems of Equations - Elimination/Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

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.

Front

What is the elimination method?

Back

A technique for solving systems of equations by removing one variable, making it easier to solve for the other.

Front

What is the substitution method?

Back

A technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What is the first step in using elimination?

Back

Align the equations so that corresponding variables are in the same column.

Front

How do you eliminate a variable in the elimination method?

Back

You can multiply one or both equations by a number to make the coefficients of one variable opposites.

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.

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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 check your solution for a system of equations?

Back

Substitute the values back into the original equations to see if they hold true.

Front

What is the graphical representation of a system of equations?

Back

The solution is where the graphs of the equations intersect.