Graphing 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 point(s) where the equations intersect.

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What does it mean to graph a system of equations?

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Graphing a system of equations involves plotting the equations on a coordinate plane to visually identify the point(s) of intersection, which represent the solution(s) to the system.

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What is the solution to a system of equations?

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The solution to a system of equations is the set of values for the variables that satisfy all equations in the system simultaneously.

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

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A system of equations has no solution if the lines represented by the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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A system of equations has infinitely many solutions if the equations represent the same line, meaning every point on the line is a 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 to find the values of the variables.

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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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What is the graphical method for solving systems of equations?

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The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where the graphs intersect.

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What is the significance of the point (6, 3) in a system of equations?

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The point (6, 3) is a solution to a system of equations, meaning it satisfies all equations in the system.

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How do you check if a point is a solution to a system of equations?

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To check if a point is a solution, substitute the x and y values of the point into each equation of the system. If the equations hold true, the point is a solution.