Test Solve Systems of Equations Using Elimin., Subst., Graph

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 to solve a system of equations by substitution?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What does it mean to solve a system of equations by elimination?

Back

It involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical representation of a system of equations?

Back

The solutions are represented by the points where the lines of the equations intersect on a graph.

Front

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

Back

It means the system has no solution, as the lines never intersect.

Front

What does it mean if two lines overlap when graphing a system of equations?

Back

It means the system has infinitely many solutions, as every point on the line is a solution.

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How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines when graphed.

Front

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

Back

Isolate one variable in one of the equations.

Front

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

Back

Align the equations and manipulate them to eliminate one variable.

Front

If a system of equations has one solution, what does that indicate about the lines?

Back

The lines intersect at exactly one point.