System 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 set of values for the variables that makes all equations true.

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What are the possible types of solutions for a system of equations?

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One solution, no solution, or infinitely many solutions.

Front

What does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

How can you solve a system of equations by graphing?

Back

Graph each equation on the same coordinate plane and identify the point(s) of intersection.

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What is the substitution method for solving systems of equations?

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Solve one equation for one variable and substitute that expression into the other equation.

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What is the elimination method for solving systems of equations?

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Add or subtract equations to eliminate one variable, making it easier to solve for the other.

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What is the graphical representation of a system of equations?

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The equations are represented as lines on a graph, and their intersection points represent the solutions.