Systems of equations review

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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 of equations?

Back

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

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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

What does it mean if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

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The lines representing the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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The lines representing the equations coincide, meaning they are the same line.

Front

How do you determine if a system of equations can be solved by graphing?

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If both equations can be easily graphed and are linear, they can be solved by graphing.

Front

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

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Make sure at least one equation is solved for one variable.

Front

In the equation x + y = 33, what do x and y represent in a word problem about ages?

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x represents one person's age and y represents another person's age.