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.

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What is a solution to a system of equations?

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

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What is the graphical representation of a system of equations?

Back

The intersection point(s) of the lines representing the equations on a graph.

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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.

Front

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

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

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What is the substitution method in solving systems of equations?

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

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What is the elimination method in solving systems of equations?

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

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What is a consistent system of equations?

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A system that has at least one solution.