Solving Systems 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.

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What does it mean to solve a system by substitution?

Back

To solve one equation for one variable and then substitute that expression into the other equation.

Front

What does it mean to solve a system 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 elimination method?

Back

A method for solving systems of equations by eliminating one variable, allowing for the solution of the remaining variable.

Front

What is the substitution method?

Back

A method for solving systems of equations where one equation is solved for one variable, which is then substituted into the other equation.

Front

How do you determine which variable to eliminate in a system of equations?

Back

Choose the variable that can be easily eliminated by adding or subtracting the equations.

Front

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

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Solve one of the equations for one variable in terms of the other variable.

Front

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

Back

Align the equations so that like terms are in the same column, and then manipulate the equations to eliminate one variable.

Front

If you have the equations 4x + 4y = 4 and 3x + 4y = 10, what is the first step in elimination?

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Subtract the second equation from the first to eliminate y.

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What does it mean if a system of equations has no solution?

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The lines represented by the equations are parallel and never intersect.