Systems of Equations Basics Review

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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 a unique solution?

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A unique solution occurs 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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No solution occurs 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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Infinitely many solutions occur when the equations represent the same line, meaning they intersect at every point on that line.

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How do you find the solution to a system of equations graphically?

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To find the solution graphically, plot both equations on the same graph and identify the point(s) where they intersect.

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

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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 and 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, add or subtract the equations to eliminate one variable, making it easier to solve for the other.