System 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.

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What does it mean for a system of equations to have one solution?

Back

It means that the equations intersect at exactly one point on the graph.

Front

What does it mean for a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

How do you find the y-coordinate of the solution in a system of equations?

Back

Substitute the x-coordinate of the solution into one of the original equations.

Front

What is the graphical representation of a system of equations?

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The solution is represented by the point(s) where the graphs of the equations intersect.

Front

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

Back

Isolate one variable in one of the equations.

Front

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

Back

Align the equations and manipulate them to eliminate one variable.