Algebra* Unit 4 Test Review 2023-24

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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 to the system is the point(s) where the equations intersect.

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How do you solve a system of equations using substitution?

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To solve a system of equations using substitution, solve one equation for one variable and then substitute that expression into the other equation.

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What does it mean for a system of equations to be consistent?

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A consistent system of equations has at least one solution, meaning the lines represented by the equations intersect at one or more points.

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What is the graphical representation of a system of inequalities?

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The graphical representation of a system of inequalities shows the regions that satisfy all inequalities, typically shaded areas on a coordinate plane.

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What is the purpose of manipulating equations in a system?

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Manipulating equations in a system helps to isolate variables, making it easier to find solutions or to express one variable in terms of another.

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What is the significance of the slope in a linear equation?

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The slope of a linear equation indicates the steepness of the line and the direction of the relationship between the variables (positive slope means increasing, negative slope means decreasing).

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

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To determine the solution to a system of equations graphically, plot both equations on the same coordinate plane and identify the point(s) where they intersect.

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What is the standard form of a linear equation?

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The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

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What is the process of simplifying a polynomial expression?

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Simplifying a polynomial expression involves combining like terms and performing any necessary arithmetic operations to reduce the expression to its simplest form.

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What does it mean for a solution to be a feasible region in linear programming?

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A feasible region in linear programming is the set of all possible points that satisfy the constraints of the problem, typically represented as a polygon on a graph.