Algebra 1 EOC Review - Category #3

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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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How do you represent a relationship between two quantities in algebra?

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You can represent a relationship using variables, equations, or inequalities. For example, if a drummer wrote d songs and a guitarist wrote g songs, you can express their relationship with equations.

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What does it mean if a slope is zero in a linear equation?

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A slope of zero means the line is horizontal, indicating that the y-value remains constant regardless of the x-value.

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What is the formula for finding the length of a line segment in a coordinate plane?

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What is the meaning of 'twice the number of songs'?

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How do you set up an equation from a word problem?

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Identify the variables, translate the relationships and conditions into mathematical expressions, and then combine them into an equation.

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What is the significance of the total in a word problem?

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The total often serves as a constraint that helps to form an equation or system of equations that must be satisfied.

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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 if the lines represented by the equations are parallel and never intersect.

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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 coordinate plane and identify the point(s) where they intersect.