Systems of Equations Flashcard - All Methods

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What is a system of equations?

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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 a unique solution?

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It means there is exactly one set of values for the variables that satisfies all equations in the system.

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

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It means that there are no values for the variables that can satisfy all equations in the system, often represented by parallel lines.

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

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It means that there are an infinite number of values for the variables that satisfy all equations, often represented by the same line.

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How do you solve a system of equations using substitution?

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1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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How do you solve a system of equations using elimination?

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1. Align the equations. 2. Multiply one or both equations to get opposite coefficients for one variable. 3. Add or subtract the equations to eliminate that variable.

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What is the graphical representation of a system of equations?

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The solution is where the graphs of the equations intersect.

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What is the solution to the system: 5x + y = 22 and 2x - y = 6?

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(4, 2)

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What is the solution to the system: 2x + y = -1 and -4x + 6y = 42?

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(-3, 5), x = -3 and y = 5.

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

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If the lines representing the equations are parallel, they will never intersect, indicating no solution.