Formulate 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 methods can be used to solve a system of equations?

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Common methods include substitution, elimination, and graphing.

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What is the substitution method in 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.

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

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A system has no solution if the equations represent parallel lines, meaning they have the same slope but different y-intercepts.

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How do you determine if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning they are equivalent.

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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. It can be written in the form Ax + By = C, where A, B, and C are constants.

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

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Coefficients determine the slope and position of the lines represented by the equations, affecting the solution set.

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How can you represent a word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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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).