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.

Front

What does it mean if a system has no solution?

Back

The lines represented by 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 there are countless points of intersection.

Front

How can you determine if a system has one solution?

Back

If the lines intersect at exactly one point.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that value 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

What is a consistent system?

Back

A system of equations that has at least one solution.