Solving 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 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 has one solution when the lines represented by 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 has no solution when the lines represented by 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 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 do you solve a system of equations by substitution?

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To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

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How do you solve a system of equations by elimination?

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To solve by elimination, manipulate the equations to eliminate one variable, allowing you to solve for the other 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 on a coordinate plane, where the intersection points represent the solutions.

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

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How do you find the x-coordinate of the intersection of two lines?

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What is the significance of the coefficients in a system of equations?

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The coefficients determine the slope and position of the lines represented by the equations.