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. The solution is the point(s) where the equations intersect.

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What does it mean to solve a system of equations graphically?

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Solving a system of equations graphically involves plotting the equations on a graph and identifying the point(s) where they intersect, which represents the solution.

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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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What is the solution to the system: y = 2x + 1 and y = 4x - 1?

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(1, 3)

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What is the solution to the system: x - 3y = -13 and 4x + 2y = 4?

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(-1, 4)

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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 they have no points of intersection, indicating that the system has no solution.

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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, they lie on top of each other, meaning there are infinitely many solutions to the system.

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How can you check if your solution to a system of equations is correct?

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You can check your solution by substituting the values back into the original equations to see if they hold true.

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What is the graphical representation of the solution to a system of equations?

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The graphical representation of the solution is the point(s) where the graphs of the equations intersect.