Solve 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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How do you represent a real-world problem as a system of equations?

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Identify the variables, formulate equations based on the relationships described in the problem, and ensure the equations reflect the constraints and conditions given.

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What is the substitution method for solving systems of equations?

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

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What is the elimination method for 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 method for solving systems of equations?

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The graphical method involves plotting the equations on a graph and identifying the point(s) where the lines intersect, which represent the solution(s) to the system.

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How can you check the solution of a system of equations?

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You can check the solution by substituting the values back into the original equations to see if they satisfy all equations.

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What is the significance of the coefficients in a system of equations?

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The coefficients represent the relationship between the variables in the equations, indicating how much one variable affects the other.

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What is a linear equation?

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A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.