Basic Systems of Equations

Front

What is a system of equations?

Back

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

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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.

Front

What is a solution to a system of equations?

Back

A pair of values (x, y) that makes all equations in the system true.

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What does it mean if a system has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, so every point on the line is a solution.

Front

How can you determine if a system has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the graphs of the equations on a coordinate plane.

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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 value into the other equation.

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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 for two lines to be coincident?

Back

They lie on top of each other, representing infinitely many solutions.