Solving Systems of Linear Equations

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What is a system of linear equations?

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A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

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What are the three methods to solve systems of linear equations?

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The three methods are graphing, substitution, and elimination.

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What does it mean to solve a system of equations using elimination?

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

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How do you determine if a system of equations has an infinite number of solutions?

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A system has an infinite number of solutions if the equations represent the same line, meaning they are dependent.

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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 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 they intersect.

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If a system of equations has no solution, what does that indicate about the lines represented by the equations?

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If there is no solution, the lines are parallel and will never intersect, indicating they are inconsistent.

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What is the first step in using the elimination method?

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The first step is to align the equations and decide which variable to eliminate.

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How do you multiply an equation to facilitate elimination?

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You multiply the entire equation by a number that will make the coefficients of one variable equal in both equations.

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