System of Linear and Nonlinear Equations

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What is a system of linear equations?

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A system of linear equations is a collection of one or more linear equations involving the same variables. The solution is the set of values that satisfy all equations in the system.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is a system of nonlinear equations?

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A system of nonlinear equations is a set of equations where at least one equation is nonlinear. Solutions are points that satisfy all equations simultaneously.

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CCSS.HSA.REI.C.7

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How do you find the intersection of a linear and a nonlinear equation graphically?

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To find the intersection, graph both equations on the same coordinate plane and identify the points where the curves intersect.

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CCSS.HSA.REI.C.7

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

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A system of equations is consistent if there is at least one solution. It can have either one solution (independent) or infinitely many solutions (dependent).

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CCSS.8.EE.C.8B

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

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A system of equations is inconsistent if there are no solutions, meaning the equations represent parallel lines that never intersect.

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CCSS.8.EE.C.8A

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What is the quadratic formula?

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CCSS.HSA-REI.B.4B

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How do you solve a system of equations using 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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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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CCSS.HSF-IF.C.7A

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What is the graphical representation of a linear equation?

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The graph of a linear equation is a straight line. The slope indicates the steepness, and the y-intercept indicates where the line crosses the y-axis.

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What is the significance of the discriminant in a quadratic equation?

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CCSS.HSA-REI.B.4B