System 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 is the point(s) where the equations intersect.

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What does it mean for a system of equations to have one solution?

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A system of equations has one solution when the graphs of the equations intersect at exactly one point.

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What does it mean for a system of equations to have no solution?

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A system of equations has no solution when the graphs of the equations are parallel and never intersect.

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What does it mean for a system of equations to have infinitely many solutions?

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A system of equations has infinitely many solutions when the equations represent the same line, meaning they intersect at every point on that line.

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How can you determine the solution to a system of equations graphically?

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You can determine the solution by graphing the equations and identifying the point(s) where the lines intersect.

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What is the substitution method for solving a system 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 for solving a system 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 significance of the x-axis and y-axis in a graph of a system of equations?

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The x-axis typically represents the independent variable, while the y-axis represents the dependent variable. The intersection of the two axes helps to visualize the solution.

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How do you interpret the solution (1, 3) in the context of a system of equations?

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The solution (1, 3) means that when x = 1 and y = 3, both equations in the system are satisfied.

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What does it mean if two lines in a graph are parallel?

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If two lines are parallel, it means they have the same slope but different y-intercepts, indicating that the system of equations has no solution.