Systems of Equations Elimination

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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 point(s) where the equations intersect.

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What does it mean to solve a system of equations by substitution?

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Solving by substitution 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 other variable.

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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 manipulate them (if necessary) so that adding or subtracting them will eliminate one variable.

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

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To check the solution, substitute the values of the variables back into the original equations to see if they hold true.

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What is the graphical interpretation of a system of equations?

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The graphical interpretation involves plotting the equations on a coordinate plane; the solution is the point where the lines intersect.

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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 there is no solution to the system, as the lines never intersect.

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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, it means there are infinitely many solutions, as every point on the line is a solution.

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How can you identify which method to use for solving a system of equations?

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Consider the coefficients of the variables; if they are easily manipulated to eliminate a variable, use elimination. If one variable is easily isolated, use substitution.

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