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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

Back

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

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

Back

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

Tags

CCSS.8.EE.C.8A

Front

What is the solution to a system of equations?

Back

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

Tags

CCSS.8.EE.C.8B

Front

Define a nonlinear equation.

Back

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.

Tags

CCSS.8.F.A.3

Front

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

Back

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

Tags

CCSS.8.EE.C.8B

Front

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

Back

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

Tags

CCSS.8.EE.C.8A

Front

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

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a quadratic equation?

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