System of Linear and Nonlinear Equations

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Define a system of linear equations.

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A system of linear equations is a collection of two or more linear equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

Front

What is the graphical representation of a linear equation in two variables?

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The graphical representation of a linear equation in two variables is a straight line on a Cartesian plane.

Front

What does it mean for a system of equations to have no solution?

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A system of equations has no solution when the lines representing the equations are parallel and never intersect.

Front

What is the solution to a system of equations?

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The solution to a system of equations is the point(s) where the graphs of the equations intersect.

Front

Define a nonlinear equation.

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A nonlinear equation is an equation that does not form a straight line when graphed, often involving variables raised to a power other than one or involving products of variables.

Front

What is the significance of the point of intersection in a system of equations?

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The point of intersection represents the values of the variables that satisfy all equations in the system.

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How do you determine if a system of equations is consistent or inconsistent?

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A system is consistent if it has at least one solution (intersecting lines) and inconsistent if it has no solutions (parallel lines).

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What is the method of substitution in solving systems of equations?

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The method of substitution involves solving one equation for one variable and substituting that expression into the other equation.

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What is the method of elimination in solving systems of equations?

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The method of elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is a quadratic equation?

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