Systems of Equations

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

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

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A system of equations has a unique 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 if two equations are equivalent?

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Two equations are equivalent if they have the same solution set, meaning they represent the same line when graphed.

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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 intersection of the lines or curves represented by the equations on a coordinate plane.

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What is the substitution method for 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 for 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 perimeter of a rectangle in terms of its length and width?

Back

The perimeter P of a rectangle is given by the formula P = 2(length + width).

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How do you express the length of a rectangle in terms of its width if the length is triple the width?

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If the length y is triple the width x, it can be expressed as y = 3x.