Solving Systems of Equations-Review

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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 that are solved together.

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What does it mean to eliminate a variable in a system of equations?

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To eliminate a variable means to manipulate the equations in such a way that one variable is removed, allowing for the solution of the remaining variable.

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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 other 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, which means they have the same slope but different y-intercepts.

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What does it mean if two lines intersect at a point in a system of equations?

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If two lines intersect at a point, it means there is a unique solution to the system of equations, represented by the coordinates of the intersection point.

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations is the plot of the equations on a coordinate plane, where the solutions are the points of intersection.

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What is the significance of the slopes of lines in a system of equations?

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The slopes of the lines indicate the relationship between the variables; equal slopes suggest parallel lines, while different slopes suggest intersection.

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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 hold true.

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What is a consistent system of equations?

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A consistent system is one that has at least one solution, which can be either unique or infinitely many.