Systems of Equations Graphing (Math)

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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 if a system of equations has no solution?

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A system of equations has no solution when 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 one solution?

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A system of equations has one solution when the lines represented by the equations intersect at exactly one point.

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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 when the equations represent the same line, meaning they overlap completely.

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

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You can determine the solution of a system of equations graphically by plotting the equations on a coordinate plane and identifying the point(s) where the lines intersect.

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What is the graphical representation of a system of equations with no solution?

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The graphical representation of a system of equations with no solution consists of two parallel lines that never meet.

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What is the graphical representation of a system of equations with one solution?

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The graphical representation of a system of equations with one solution consists of two lines that intersect at a single point.

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What is the graphical representation of a system of equations with infinitely many solutions?

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The graphical representation of a system of equations with infinitely many solutions consists of two overlapping lines.

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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.