Solving Systems of Equations

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

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What are the three main methods for solving systems of equations?

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The three main methods are: 1) Graphing, 2) Substitution, 3) Elimination.

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How do you solve a system of equations using the substitution method?

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To solve using substitution, solve one equation for one variable, then substitute that expression into the other equation.

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What is the elimination method in solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

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What does it mean for a system of equations to be consistent?

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A consistent system has at least one solution, meaning the equations intersect at one or more points.

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

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What is the graphical representation of a system of equations?

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The graphical representation involves plotting each equation on a coordinate plane and identifying the point(s) where they intersect.

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What is the significance of the point of intersection in a system of equations?

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The point of intersection represents the solution to the system, indicating the values of the variables that satisfy all equations.

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How do you determine which variable to eliminate in the elimination method?

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Choose the variable that can be easily eliminated, often based on the coefficients. The variable with the least common multiple (LCM) is a good candidate.

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What is the substitution method best used for?

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The substitution method is best used when one equation is already solved for one variable, making it straightforward to substitute into the other equation.