Solving Systems of Equations

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 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

When is substitution the best method to use?

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When one equation is already solved for one variable, making it easy to substitute.

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When is elimination the best method to use?

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When both equations are in standard form and can be easily manipulated to eliminate a variable.

Front

Solve the system: 2x + 3y = 6 and x - y = 1.

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(3, 0) is the solution.

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Solve the system: 4x - y = 7 and 2x + 3y = 12.

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(3, 2) is the solution.

Front

What is the graphical method for solving systems of equations?

Back

Plotting both equations on a graph and identifying the point(s) where they intersect.

Front

What does it mean if two lines are parallel in a system of equations?

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The system has no solution because the lines never intersect.