System Of Equations

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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

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

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It means there is exactly one set of values for the variables that satisfies all equations in the system.

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

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It means that there are no values for the variables that can satisfy all equations in the system, often because the lines are parallel.

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

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It means that there are an infinite number of values for the variables that satisfy all equations, often because the equations represent the same line.

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How do you solve a system of equations using the substitution method?

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1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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How do you solve a system of equations using the elimination method?

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1. Align the equations. 2. Add or subtract the equations to eliminate one variable. 3. Solve for the remaining variable.

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What is the graphical representation of a system of equations?

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The graphical representation consists of lines or curves on a coordinate plane, where the intersection points represent the solutions.

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What is the importance of the point of intersection in a system of equations?

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The point of intersection represents the solution to the system, indicating the values of the variables that satisfy all equations.

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What is the slope-intercept form of a linear equation?

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The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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How can you determine if two lines are parallel from their equations?

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Two lines are parallel if they have the same slope but different y-intercepts.