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 to the system is the set of values that satisfy all equations simultaneously.

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What does it mean to solve a system of equations graphically?

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Solving a system of equations graphically involves plotting the equations on a coordinate plane and identifying the point(s) where the lines intersect, which represents the solution(s) to the system.

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of the variables.

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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 if two lines are parallel in a system of equations?

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If two lines are parallel, it means they have the same slope and will never intersect, indicating that the system has no solution.

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What does it mean if two lines coincide in a system of equations?

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If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system.

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How can you determine the solution to a system of equations algebraically?

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To determine the solution algebraically, you can use either the substitution or elimination method to find the values of the variables that satisfy both equations.

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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 of equations, where the values of the variables satisfy all equations in the system.

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What is a consistent system of equations?

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A consistent system of equations has at least one solution, which can be either a single point of intersection or infinitely many solutions.

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What is an inconsistent system of equations?

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An inconsistent system of equations has no solutions, typically represented by parallel lines that do not intersect.