Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

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 are the three possible outcomes when solving a system of equations?

Back

One solution, no solution, or infinitely many solutions.

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What is the substitution method?

Back

A method for solving a system of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method?

Back

A method for solving a system of equations by adding or subtracting equations to eliminate one variable.

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect.

Front

How do you determine if a system of equations has infinitely many solutions?

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

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What is the graphical representation of a system of equations?

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The points where the graphs of the equations intersect represent the solutions.

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What does it mean for a variable to be 'alone' in an equation?

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It means that the variable is isolated on one side of the equation, making it easier to solve for.

Front

How can you tell which variable is easiest to isolate in an equation?

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Look for the variable with the least number of terms or coefficients.