Solving 3-variable systems REVIEW

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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 to solve a system of equations by elimination?

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Elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variables.

Front

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

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Substitution involves solving one equation for a variable and then substituting that expression into another equation.

Front

What is the graphical interpretation of a system of equations?

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The solutions to a system of equations can be represented as the points where the graphs of the equations intersect.

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What is a unique solution in a system of equations?

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A unique solution occurs when the lines representing the equations intersect at exactly one point.

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What is an infinite solution in a system of equations?

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Infinite solutions occur when the equations represent the same line, meaning there are countless points of intersection.

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What is no solution in a system of equations?

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No solution occurs when the lines representing the equations are parallel and never intersect.

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How do you represent a system of equations algebraically?

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A system of equations can be represented in the form: 1. ax + by = c 2. dx + ey = f 3. gx + hy = i, where a, b, c, d, e, f, g, h, i are constants.

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

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The first step is to align the equations so that like terms are in the same column, making it easier to eliminate a variable.

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

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The first step is to solve one of the equations for one variable in terms of the others.